Maths-
General
Easy

Question

Write each function in standard form .
F(x)= -2(x-9)2 +15

Hint:

The standard quadratic form is ax2+bx+c=y, the vertex form of a quadratic equation is y=a(x−h)2+k.

The correct answer is: f(x) = -2x2 + 36x - 147.


    We have given the function in Vertex form , we have to convert it into standard form.
    F(x)= -2(x-9)2 +15
    On further solving this function we will get
    F(x) = -2 ( x2 - 18x + 81 ) + 15
    = -2x2 + 36x - 162 + 15
    = -2x2 + 36x - 147
    Therefore, the standard form of given function is f(x) = -2x2 + 36x - 147.

    Related Questions to study

    General
    Maths-

    Write each function in standard form . F(x)= 4(x+1)2 -3

    Hint :- The standard quadratic form is ax2+bx+c=y, the vertex form of a quadratic equation is y=a(x−h)2+k.
    Solution :- We have given the function in Vertex form , we have to convert it into standard form.
                          F(x)= 4(x+1)2 -3
    On further solving this function we will get
    F(x) = 4 ( x2 + 2x + 1 ) – 3
    = 4x2 + 8x + 4 – 3
    = 4x2 + 8x + 1
    Therefore, the standard form of given function is f(x) = 4x2 + 8x + 1.
                                       
    Q39:
    Complex Level : Hard
    Blooms Level: Understanding
    Write each function in standard form . F(x)= 0.1 (x-2)2 – 0.1
    Hint :- The standard quadratic form is ax2+bx+c=y, the vertex form of a quadratic equation is y=a(x−h)2+k.
    Solution :- We have given the function in Vertex form , we have to convert it into standard form.
    F(x)= 0.1(x-2)2 - 0.1
    On further solving this function we will get
    F(x) = 0.1 ( x2 - 4x + 4 ) – 0.1
    = 0.1x2 – 0.4x + 0.4 – 0.1
    = 0.1x2 -0.4x + 0.3
    Therefore, the standard form of given function is f(x) =0.1x2 -0.4x + 0.3.

    Write each function in standard form . F(x)= 4(x+1)2 -3

    Maths-General
    Hint :- The standard quadratic form is ax2+bx+c=y, the vertex form of a quadratic equation is y=a(x−h)2+k.
    Solution :- We have given the function in Vertex form , we have to convert it into standard form.
                          F(x)= 4(x+1)2 -3
    On further solving this function we will get
    F(x) = 4 ( x2 + 2x + 1 ) – 3
    = 4x2 + 8x + 4 – 3
    = 4x2 + 8x + 1
    Therefore, the standard form of given function is f(x) = 4x2 + 8x + 1.
                                       
    Q39:
    Complex Level : Hard
    Blooms Level: Understanding
    Write each function in standard form . F(x)= 0.1 (x-2)2 – 0.1
    Hint :- The standard quadratic form is ax2+bx+c=y, the vertex form of a quadratic equation is y=a(x−h)2+k.
    Solution :- We have given the function in Vertex form , we have to convert it into standard form.
    F(x)= 0.1(x-2)2 - 0.1
    On further solving this function we will get
    F(x) = 0.1 ( x2 - 4x + 4 ) – 0.1
    = 0.1x2 – 0.4x + 0.4 – 0.1
    = 0.1x2 -0.4x + 0.3
    Therefore, the standard form of given function is f(x) =0.1x2 -0.4x + 0.3.
    General
    Maths-

    Compare each function to f, shown in the table. Which function has lesser minimum value? Explain


    h(x) = x2 + x – 3.5

    We have given two functions f(x) and h(x).
    h(x) = x2 + x – 3.5
    For f(x) , minimum value of the function will be the y-coordinate of the given point which has minimum values
    (1,0) , (2,-3) , (3,-4) , (4,-3) (5,0)
    In the given points minimum value of is (3,-4)
    So, the ,minimum value of f(x) is -4.
    In h(x) = x2 + x – 3.5,  a= 1, b= 1, and c = -3.5. So, the equation for the axis of symmetry is given by

    x = −(1)/2(1)

    x = -1/2

    x = -0.5
    The equation of the axis of symmetry for h(x) = x2 + x – 3.5 is x = -0.5.
    The x coordinate of the vertex is the same:

    h =-0.5
    The y coordinate of the vertex is :

    k = f(h)

    k = h2 + h – 3.5

    k = (-0.5)2 + (-0.5) – 3.5

    k = 0.25 – 0.5 – 3.5

    k = -3.75
    Therefore, the vertex is (-0.5 , -3.75)
    The minimum value of g(x) will be the y-coordinate of vertex = -3.75

    Compare each function to f, shown in the table. Which function has lesser minimum value? Explain


    h(x) = x2 + x – 3.5

    Maths-General
    We have given two functions f(x) and h(x).
    h(x) = x2 + x – 3.5
    For f(x) , minimum value of the function will be the y-coordinate of the given point which has minimum values
    (1,0) , (2,-3) , (3,-4) , (4,-3) (5,0)
    In the given points minimum value of is (3,-4)
    So, the ,minimum value of f(x) is -4.
    In h(x) = x2 + x – 3.5,  a= 1, b= 1, and c = -3.5. So, the equation for the axis of symmetry is given by

    x = −(1)/2(1)

    x = -1/2

    x = -0.5
    The equation of the axis of symmetry for h(x) = x2 + x – 3.5 is x = -0.5.
    The x coordinate of the vertex is the same:

    h =-0.5
    The y coordinate of the vertex is :

    k = f(h)

    k = h2 + h – 3.5

    k = (-0.5)2 + (-0.5) – 3.5

    k = 0.25 – 0.5 – 3.5

    k = -3.75
    Therefore, the vertex is (-0.5 , -3.75)
    The minimum value of g(x) will be the y-coordinate of vertex = -3.75

    General
    Maths-

    Compare each function to f, shown in the table. Which function has lesser minimum value? Explain

    g(x) = 2x2 + 8x + 3

    Solution:- We have given two functions f(x) and g(x).
    g(x) = 2x2 + 8x + 3
    For f(x) , minimum value of the function will be the y-coordinate of the given point which has minimum values
    (1,0) , (2,-3) , (3,-4) , (4,-3) (5,0)
    In the given points minimum value of is (3,-4)
    So, the ,minimum value of f(x) is -4.
    In g(x)= 2x2 + 8x + 3,  a= 2, b= 8, and c=3. So, the equation for the axis of symmetry is given by

    x = −(8)/2(2)

    x = -8/4

    x = -2
    The equation of the axis of symmetry for g(x)= 2x2 + 8x + 3 is x = -2.
    The x coordinate of the vertex is the same:

    h =-2
    The y coordinate of the vertex is :

    k = f(h)

    k = 2h2 + 8h + 3

    k = 2(-2)2 + 8(-2) + 3

    k = 8 - 16 + 3

    k = -5
    Therefore, the vertex is (-2 , -5)
    The minimum value of g(x) will be the y-coordinate of vertex = -5

    Compare each function to f, shown in the table. Which function has lesser minimum value? Explain

    g(x) = 2x2 + 8x + 3

    Maths-General
    Solution:- We have given two functions f(x) and g(x).
    g(x) = 2x2 + 8x + 3
    For f(x) , minimum value of the function will be the y-coordinate of the given point which has minimum values
    (1,0) , (2,-3) , (3,-4) , (4,-3) (5,0)
    In the given points minimum value of is (3,-4)
    So, the ,minimum value of f(x) is -4.
    In g(x)= 2x2 + 8x + 3,  a= 2, b= 8, and c=3. So, the equation for the axis of symmetry is given by

    x = −(8)/2(2)

    x = -8/4

    x = -2
    The equation of the axis of symmetry for g(x)= 2x2 + 8x + 3 is x = -2.
    The x coordinate of the vertex is the same:

    h =-2
    The y coordinate of the vertex is :

    k = f(h)

    k = 2h2 + 8h + 3

    k = 2(-2)2 + 8(-2) + 3

    k = 8 - 16 + 3

    k = -5
    Therefore, the vertex is (-2 , -5)
    The minimum value of g(x) will be the y-coordinate of vertex = -5

    parallel
    General
    Maths-

    Find the axis of symmetry, vertex and y-intercept of the function
    f(x) = -2x2 + 16x + 40

    This quadratic function is in standard form, f(x)=ax2+bx+c.
    For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
    In f(x)= -2x2 + 16x + 40,  a= -2, b= 16, and c= 40. So, the equation for the axis of symmetry is given by

    x = −(16)/2(-2)

    x = -16/-4

    x = 4
    The equation of the axis of symmetry for f(x)= -2x2 + 16x + 40 is x = 4.
    The x coordinate of the vertex is the same:

    h = 4
    The y coordinate of the vertex is :

    k = f(h)

    k = -2h2 + 16h + 40

    k = -2(4)2 + 16(4) + 40

    k = -32 + 64 + 40

    k = 72
    Therefore, the vertex is (4 , 72)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

    y = -2(0)2 + 16(0) + 40

    y = 0 + 0 + 40

    y = 40
    Therefore, Axis of symmetry is x = 4
    Vertex is (4 , 72)
    Y- intercept is 40.

    Find the axis of symmetry, vertex and y-intercept of the function
    f(x) = -2x2 + 16x + 40

    Maths-General
    This quadratic function is in standard form, f(x)=ax2+bx+c.
    For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
    In f(x)= -2x2 + 16x + 40,  a= -2, b= 16, and c= 40. So, the equation for the axis of symmetry is given by

    x = −(16)/2(-2)

    x = -16/-4

    x = 4
    The equation of the axis of symmetry for f(x)= -2x2 + 16x + 40 is x = 4.
    The x coordinate of the vertex is the same:

    h = 4
    The y coordinate of the vertex is :

    k = f(h)

    k = -2h2 + 16h + 40

    k = -2(4)2 + 16(4) + 40

    k = -32 + 64 + 40

    k = 72
    Therefore, the vertex is (4 , 72)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

    y = -2(0)2 + 16(0) + 40

    y = 0 + 0 + 40

    y = 40
    Therefore, Axis of symmetry is x = 4
    Vertex is (4 , 72)
    Y- intercept is 40.

    General
    Maths-

    Find the axis of symmetry, vertex and y-intercept of the function
    f(x) = x2 - 6x + 12

    This quadratic function is in standard form, f(x)=ax2+bx+c.
    For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
    In f(x)= x2 - 6x + 12,  a= 1, b= -6, and c= 12. So, the equation for the axis of symmetry is given by

    x = −(-6)/2(1)

    x = 6/2

    x = 3
    The equation of the axis of symmetry for f(x)= x2 - 6x + 12 is x = 3.
    The x coordinate of the vertex is the same:

    h = 3
    The y coordinate of the vertex is :

    k = f(h)

    k = h2 – 6h + 12

    k = (3)2 - 6(3) + 12

    k = 9 – 18 + 12

    k = 3
    Therefore, the vertex is (3 , 3)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

    y = (0)2 - 6(0) + 12

    y = 0 + 0 + 12

    y = 12
    Therefore, Axis of symmetry is x = 3
    Vertex is (3 , 3)
    Y- intercept is 12.

    Find the axis of symmetry, vertex and y-intercept of the function
    f(x) = x2 - 6x + 12

    Maths-General
    This quadratic function is in standard form, f(x)=ax2+bx+c.
    For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
    In f(x)= x2 - 6x + 12,  a= 1, b= -6, and c= 12. So, the equation for the axis of symmetry is given by

    x = −(-6)/2(1)

    x = 6/2

    x = 3
    The equation of the axis of symmetry for f(x)= x2 - 6x + 12 is x = 3.
    The x coordinate of the vertex is the same:

    h = 3
    The y coordinate of the vertex is :

    k = f(h)

    k = h2 – 6h + 12

    k = (3)2 - 6(3) + 12

    k = 9 – 18 + 12

    k = 3
    Therefore, the vertex is (3 , 3)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

    y = (0)2 - 6(0) + 12

    y = 0 + 0 + 12

    y = 12
    Therefore, Axis of symmetry is x = 3
    Vertex is (3 , 3)
    Y- intercept is 12.

    General
    Maths-

    Find the axis of symmetry, vertex and y-intercept of the function
    f(x) = 4x2 + 12x + 5

    This quadratic function is in standard form, f(x)=ax2+bx+c.
    For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
    In f(x)= = 4x2 + 12x + 5, a= 4, b= 12, and c= 5. So, the equation for the axis of symmetry is given by

    x = −(12)/2(4)

    x = -12/8

    x = -3/2 = -1.5
    The equation of the axis of symmetry for f(x)= = 4x2 + 12x + 5 is x = -1.5.
    The x coordinate of the vertex is the same:

    h = -1.5
    The y coordinate of the vertex is :

    k = f(h)

    k = 4h2 + 12h + 5

    k = 4(-1.5)2 + 12(-1.5) + 5

    k = 9 – 18 + 5

    k = -4
    Therefore, the vertex is (-1.5 , -4)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

    y = 4(0)2 + 12(0) + 5

    y = 0 + 0 + 5

    y = 5
    Therefore, Axis of symmetry is x = -1.5
    Vertex is ( -1.5 , -4)
    Y- intercept is 5.

    Find the axis of symmetry, vertex and y-intercept of the function
    f(x) = 4x2 + 12x + 5

    Maths-General
    This quadratic function is in standard form, f(x)=ax2+bx+c.
    For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
    In f(x)= = 4x2 + 12x + 5, a= 4, b= 12, and c= 5. So, the equation for the axis of symmetry is given by

    x = −(12)/2(4)

    x = -12/8

    x = -3/2 = -1.5
    The equation of the axis of symmetry for f(x)= = 4x2 + 12x + 5 is x = -1.5.
    The x coordinate of the vertex is the same:

    h = -1.5
    The y coordinate of the vertex is :

    k = f(h)

    k = 4h2 + 12h + 5

    k = 4(-1.5)2 + 12(-1.5) + 5

    k = 9 – 18 + 5

    k = -4
    Therefore, the vertex is (-1.5 , -4)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

    y = 4(0)2 + 12(0) + 5

    y = 0 + 0 + 5

    y = 5
    Therefore, Axis of symmetry is x = -1.5
    Vertex is ( -1.5 , -4)
    Y- intercept is 5.

    parallel
    General
    Maths-

    Find the axis of symmetry, vertex and y-intercept of the function
    f(x) = 5x2 + 5x + 12

    This quadratic function is in standard form, f(x)=ax2+bx+c.
    For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
    In f(x)= 5x2 + 5x + 12 , a= 5, b= 5, and c= 12. So, the equation for the axis of symmetry is given by

    x = −(5)/2(5)

    x = -5/10

    x = -1/2 = -0.5
    The equation of the axis of symmetry for f(x)= 5x2 + 5x + 12 is x = -0.5.
    The x coordinate of the vertex is the same:

    h = -0.5
    The y coordinate of the vertex is :

    k = f(h)

    k = 5(h)2 + 5h + 12

    k = 5(-0.5)2 + 5(-0.5) + 12

    k = 1.25 – 2.5 + 12

    k = 10.75
    Therefore, the vertex is (-0.5 , 10.75)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

    y = 5(0)2 + 5(0) + 12

    y = 0 + 0 + 12

    y = 12
    Therefore, Axis of symmetry is x = -0.5
    Vertex is ( -0.5 , 10.75)
    Y- intercept is 12.

    Find the axis of symmetry, vertex and y-intercept of the function
    f(x) = 5x2 + 5x + 12

    Maths-General
    This quadratic function is in standard form, f(x)=ax2+bx+c.
    For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
    In f(x)= 5x2 + 5x + 12 , a= 5, b= 5, and c= 12. So, the equation for the axis of symmetry is given by

    x = −(5)/2(5)

    x = -5/10

    x = -1/2 = -0.5
    The equation of the axis of symmetry for f(x)= 5x2 + 5x + 12 is x = -0.5.
    The x coordinate of the vertex is the same:

    h = -0.5
    The y coordinate of the vertex is :

    k = f(h)

    k = 5(h)2 + 5h + 12

    k = 5(-0.5)2 + 5(-0.5) + 12

    k = 1.25 – 2.5 + 12

    k = 10.75
    Therefore, the vertex is (-0.5 , 10.75)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

    y = 5(0)2 + 5(0) + 12

    y = 0 + 0 + 12

    y = 12
    Therefore, Axis of symmetry is x = -0.5
    Vertex is ( -0.5 , 10.75)
    Y- intercept is 12.

    General
    Maths-

    Find the axis of symmetry, vertex and y-intercept of the function
    f(x) = -x2 - 2x – 5

    This quadratic function is in standard form, f(x)=ax2+bx+c.
    For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
    In f(x)= -x2 - 2x – 5, a= -1, b= -2, and c= -5. So, the equation for the axis of symmetry is given by

    x = −(-2)/2(-1)

    x = 2/-2

    x = -1
    The equation of the axis of symmetry for f(x)= -x2 - 2x – 5 is x = -1.
    The x coordinate of the vertex is the same:

    h = -1
    The y coordinate of the vertex is :

    k = f(h)

    k = -(h)2 - 2(h) - 5

    k = -(-1)2 - 2(-1) - 5

    k = -1 + 2 - 5

    k = -4
    Therefore, the vertex is (-1 , -4)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

    y = -(0)2 - 2(0) - 5

    y = 0 - 0 - 5

    y = -5
    Therefore, Axis of symmetry is x = -1
    Vertex is ( -1 , -4)
    Y- intercept is -5.

    Find the axis of symmetry, vertex and y-intercept of the function
    f(x) = -x2 - 2x – 5

    Maths-General
    This quadratic function is in standard form, f(x)=ax2+bx+c.
    For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
    In f(x)= -x2 - 2x – 5, a= -1, b= -2, and c= -5. So, the equation for the axis of symmetry is given by

    x = −(-2)/2(-1)

    x = 2/-2

    x = -1
    The equation of the axis of symmetry for f(x)= -x2 - 2x – 5 is x = -1.
    The x coordinate of the vertex is the same:

    h = -1
    The y coordinate of the vertex is :

    k = f(h)

    k = -(h)2 - 2(h) - 5

    k = -(-1)2 - 2(-1) - 5

    k = -1 + 2 - 5

    k = -4
    Therefore, the vertex is (-1 , -4)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

    y = -(0)2 - 2(0) - 5

    y = 0 - 0 - 5

    y = -5
    Therefore, Axis of symmetry is x = -1
    Vertex is ( -1 , -4)
    Y- intercept is -5.

    General
    Maths-

    Find the axis of symmetry, vertex and y-intercept of the function
    f(x) = 0.4x2 + 1.6x

    This quadratic function is in standard form, f(x)=ax2+bx+c.
    For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
    In f(x)= 0.4x2 + 1.6x, a= 0.4, b= 1.6, and c= 0. So, the equation for the axis of symmetry is given by

    x = −(1.6)/2(0.4)

    x = -1.6/0.8

    x = -2
    The equation of the axis of symmetry for f(x)= 0.4x2 + 1.6x is x = -2.
    The x coordinate of the vertex is the same:

    h = -2
    The y coordinate of the vertex is :

    k = f(h)

    k = 0.4(h)2 + 1.6h

    k = 0.4(-2)2 + 1.6(-2)

    k = 1.6 – 3.2

    k = -1.6
    Therefore, the vertex is (-2 , -1.6)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

    y = 0.4(0)2 + 1.6(0)

    y = 0 + 0

    y = 0
    Therefore, Axis of symmetry is x = -2
    Vertex is ( -2 , -1.6)
    Y- intercept is 0.

    Find the axis of symmetry, vertex and y-intercept of the function
    f(x) = 0.4x2 + 1.6x

    Maths-General
    This quadratic function is in standard form, f(x)=ax2+bx+c.
    For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
    In f(x)= 0.4x2 + 1.6x, a= 0.4, b= 1.6, and c= 0. So, the equation for the axis of symmetry is given by

    x = −(1.6)/2(0.4)

    x = -1.6/0.8

    x = -2
    The equation of the axis of symmetry for f(x)= 0.4x2 + 1.6x is x = -2.
    The x coordinate of the vertex is the same:

    h = -2
    The y coordinate of the vertex is :

    k = f(h)

    k = 0.4(h)2 + 1.6h

    k = 0.4(-2)2 + 1.6(-2)

    k = 1.6 – 3.2

    k = -1.6
    Therefore, the vertex is (-2 , -1.6)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

    y = 0.4(0)2 + 1.6(0)

    y = 0 + 0

    y = 0
    Therefore, Axis of symmetry is x = -2
    Vertex is ( -2 , -1.6)
    Y- intercept is 0.

    parallel
    General
    Maths-

    Find the axis of symmetry, vertex and y-intercept of the function
    f(x) = -2x2 + 4x - 3

    This quadratic function is in standard form, f(x)=ax2+bx+c.
    For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
    In f(x)= -2x2 + 4x -3, a= -2, b= 4, and c= -3. So, the equation for the axis of symmetry is given by

    x = −(4)/2(-2)

    x = -4/-4

    x = 1
    The equation of the axis of symmetry for f(x)= 2x2 + 4x - 3 is x = 1.
    The x coordinate of the vertex is the same:
    h = 1
    The y coordinate of the vertex is :

    k = f(h)

    k = -2(h)2 + 4(h) - 3

    k = -2(1)2 + 4(1) - 3

    k = -2 + 4 - 3

    k = -1
    Therefore, the vertex is (1 , -1)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

    y = -2(0)2 + 4(0) - 3

    y = 0 + 0 - 3

    y = -3
    Therefore, Axis of symmetry is x = 1
    Vertex is ( 1 , -1)
    Y- intercept is -3.

    Find the axis of symmetry, vertex and y-intercept of the function
    f(x) = -2x2 + 4x - 3

    Maths-General
    This quadratic function is in standard form, f(x)=ax2+bx+c.
    For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
    In f(x)= -2x2 + 4x -3, a= -2, b= 4, and c= -3. So, the equation for the axis of symmetry is given by

    x = −(4)/2(-2)

    x = -4/-4

    x = 1
    The equation of the axis of symmetry for f(x)= 2x2 + 4x - 3 is x = 1.
    The x coordinate of the vertex is the same:
    h = 1
    The y coordinate of the vertex is :

    k = f(h)

    k = -2(h)2 + 4(h) - 3

    k = -2(1)2 + 4(1) - 3

    k = -2 + 4 - 3

    k = -1
    Therefore, the vertex is (1 , -1)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

    y = -2(0)2 + 4(0) - 3

    y = 0 + 0 - 3

    y = -3
    Therefore, Axis of symmetry is x = 1
    Vertex is ( 1 , -1)
    Y- intercept is -3.

    General
    Maths-

    Find the axis of symmetry, vertex and y-intercept of the function
    f(x) = 2x2 + 8x + 2

    This quadratic function is in standard form, f(x)=ax2+bx+c.
    For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
    In f(x)= 2x2 + 8x + 2, a= 2, b= 8, and c= 2. So, the equation for the axis of symmetry is given by

    x = −(8)/2(2)

    x = -8/4

    x = -2
    The equation of the axis of symmetry for f(x)= 2x2 + 8x + 2 is x = -2.
    The x coordinate of the vertex is the same:

    h = -2
    The y coordinate of the vertex is :

    k = f(h)

    k = 2(h)2 + 8(h) + 2

    k = 2(-2)2 + 8(-2) + 2

    k = 8 – 16 + 2

    k = -6
    Therefore, the vertex is (-2 , -6)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

    y = 2(0)2 + 8(0) + 2

    y = 0 + 0 + 2

    y = 2
    Therefore, Axis of symmetry is x = -2
    Vertex is ( -2 , -6)
    Y- intercept is 2.

    Find the axis of symmetry, vertex and y-intercept of the function
    f(x) = 2x2 + 8x + 2

    Maths-General
    This quadratic function is in standard form, f(x)=ax2+bx+c.
    For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.
    In f(x)= 2x2 + 8x + 2, a= 2, b= 8, and c= 2. So, the equation for the axis of symmetry is given by

    x = −(8)/2(2)

    x = -8/4

    x = -2
    The equation of the axis of symmetry for f(x)= 2x2 + 8x + 2 is x = -2.
    The x coordinate of the vertex is the same:

    h = -2
    The y coordinate of the vertex is :

    k = f(h)

    k = 2(h)2 + 8(h) + 2

    k = 2(-2)2 + 8(-2) + 2

    k = 8 – 16 + 2

    k = -6
    Therefore, the vertex is (-2 , -6)
    For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

    y = 2(0)2 + 8(0) + 2

    y = 0 + 0 + 2

    y = 2
    Therefore, Axis of symmetry is x = -2
    Vertex is ( -2 , -6)
    Y- intercept is 2.

    General
    Maths-

    Find the y-intercept of the following function
    f(x) = -0.5x2 + x + 2

    We have given a function
    f(x) = -0.5x2 + x + 2
    We will compare the given equation with the standard equation f(x)=ax2+bx+c.
    We know that for y intercept , x = 0
    So, for finding y- intercept
    f(x) = y = -0.5(0)2 + (0) + 2
    y = 2
    On comparing with the standard form y-intercept is equal to c
    y-intercept of given quadratic function is 2.

    Find the y-intercept of the following function
    f(x) = -0.5x2 + x + 2

    Maths-General
    We have given a function
    f(x) = -0.5x2 + x + 2
    We will compare the given equation with the standard equation f(x)=ax2+bx+c.
    We know that for y intercept , x = 0
    So, for finding y- intercept
    f(x) = y = -0.5(0)2 + (0) + 2
    y = 2
    On comparing with the standard form y-intercept is equal to c
    y-intercept of given quadratic function is 2.
    parallel
    General
    Maths-

    Find the y-intercept of the following function
    f(x) = - x2 – 2x + 3

    We have given a function
    f(x) = x2 – 2x + 3
    We will compare the given equation with the standard equation f(x)=ax2+bx+c.
    We know that for y intercept , x = 0
    So, for finding y- intercept
    f(x) = y = (0)2 – 2(0) + 3
    y = 3
    On comparing with the standard form y-intercept is equal to c
    y-intercept of given quadratic function is 3.

    Find the y-intercept of the following function
    f(x) = - x2 – 2x + 3

    Maths-General
    We have given a function
    f(x) = x2 – 2x + 3
    We will compare the given equation with the standard equation f(x)=ax2+bx+c.
    We know that for y intercept , x = 0
    So, for finding y- intercept
    f(x) = y = (0)2 – 2(0) + 3
    y = 3
    On comparing with the standard form y-intercept is equal to c
    y-intercept of given quadratic function is 3.
    General
    Maths-

    Find the y-intercept of the following function
    f(x) = 3x2 + 6x + 5

    We have given a function
    f(x) = 3x2 + 6x + 5
    We will compare the given equation with the standard equation f(x)=ax2+bx+c.
    We know that for y intercept , x = 0
    So, for finding y- intercept
    f(x) = y = 3(0)2 + 6(0) + 5
    y = 5
    On comparing with the standard form y-intercept is equal to c
    y-intercept of given quadratic function is 5.

    Find the y-intercept of the following function
    f(x) = 3x2 + 6x + 5

    Maths-General
    We have given a function
    f(x) = 3x2 + 6x + 5
    We will compare the given equation with the standard equation f(x)=ax2+bx+c.
    We know that for y intercept , x = 0
    So, for finding y- intercept
    f(x) = y = 3(0)2 + 6(0) + 5
    y = 5
    On comparing with the standard form y-intercept is equal to c
    y-intercept of given quadratic function is 5.
    General
    Maths-

    Find the y-intercept of the following function
    f(x) = -2x2 – 8x – 7

     We have given a function
    f(x) = 2x2 – 8x – 7
    We will compare the given equation with the standard equation f(x)=ax2+bx+c.
    We know that for y intercept , x = 0
    So, for finding y- intercept
    f(x) = y = 2(0)2 – 8(0) – 7
    y = -7
    On comparing with the standard form y-intercept is equal to c
    y-intercept of given quadratic function is -7.

    Find the y-intercept of the following function
    f(x) = -2x2 – 8x – 7

    Maths-General
     We have given a function
    f(x) = 2x2 – 8x – 7
    We will compare the given equation with the standard equation f(x)=ax2+bx+c.
    We know that for y intercept , x = 0
    So, for finding y- intercept
    f(x) = y = 2(0)2 – 8(0) – 7
    y = -7
    On comparing with the standard form y-intercept is equal to c
    y-intercept of given quadratic function is -7.
    parallel

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