Maths-
General
Easy

Question

Find the y-intercept of the following function
f(x) = 0.3x2 + 0.6x – 0.7

Hint:

For a quadratic function is in standard form, f(x)=ax2+bx+c.
The y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x=0.
 

The correct answer is: -0.7.


    We have given a function
    f(x) = 0.3x2 + 0.6x – 0.7
    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 = 0.3(0)2 + 0.6(0) – 0.7
    y = -0.7
    On comparing with the standard form y-intercept is equal to c
    y-intercept of given quadratic function is -0.7.

    Related Questions to study

    General
    Maths-

    Find the y-intercept of the following function
    f(x) = 2x2 – 4x – 6

    We have given a function
    f(x) = 2x2 – 4x – 6
    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 – 4(0) – 6
    y = -6
    On comparing with the standard form y-intercept is equal to c
    y-intercept of given quadratic function is -6.

    Find the y-intercept of the following function
    f(x) = 2x2 – 4x – 6

    Maths-General
    We have given a function
    f(x) = 2x2 – 4x – 6
    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 – 4(0) – 6
    y = -6
    On comparing with the standard form y-intercept is equal to c
    y-intercept of given quadratic function is -6.
    General
    Maths-

    Points (2, -1), (-2, 7), (1, -2), (0, -1) and (4, 7) lie on graph of a quadratic function
    1.Find axis of symmetry of graph
    2.Find the vertex
    3.Find the y-intercept
    4.Over what interval does the function increase


    We can see that the axis of symmetry passes through x= 1
    Therefore, the vertex point is (1,-2)
    Y intercept is the point at which x = 0 which is (0,-1)
    y- intercept= -1

    Points (2, -1), (-2, 7), (1, -2), (0, -1) and (4, 7) lie on graph of a quadratic function
    1.Find axis of symmetry of graph
    2.Find the vertex
    3.Find the y-intercept
    4.Over what interval does the function increase

    Maths-General

    We can see that the axis of symmetry passes through x= 1
    Therefore, the vertex point is (1,-2)
    Y intercept is the point at which x = 0 which is (0,-1)
    y- intercept= -1
    General
    Maths-

    Estimate the coordinates of the vertex of the graph of f(x) = 1.25x2 -2x -1 below. Then explain how to find the exact coordinates

    We have given a function
    f(x) = 1.25x2 -2x -1
    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)= 1.25x2 -2x -1, a= 1.25, b= -2, and c= -1. So, the equation for the axis of symmetry is given by
    x = −(-2)/2(1.25)
    x = 2/2.5
    x = 0.8
    The equation of the axis of symmetry for f(x)= 1.25x2 -2x -1 is x = 0.8.
    The x coordinate of the vertex is the same:
    h = 0.8
    The y coordinate of the vertex is :
    k = f(h)
    k = 1.25h2 -2h -1
    k = 1.25(0.8)2 - 2(0.8) - 1
    k = 0.8 - 1.6 – 1
    k = -1.8
    Therefore, the vertex is (0.8 , -1.8)

    Estimate the coordinates of the vertex of the graph of f(x) = 1.25x2 -2x -1 below. Then explain how to find the exact coordinates

    Maths-General
    We have given a function
    f(x) = 1.25x2 -2x -1
    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)= 1.25x2 -2x -1, a= 1.25, b= -2, and c= -1. So, the equation for the axis of symmetry is given by
    x = −(-2)/2(1.25)
    x = 2/2.5
    x = 0.8
    The equation of the axis of symmetry for f(x)= 1.25x2 -2x -1 is x = 0.8.
    The x coordinate of the vertex is the same:
    h = 0.8
    The y coordinate of the vertex is :
    k = f(h)
    k = 1.25h2 -2h -1
    k = 1.25(0.8)2 - 2(0.8) - 1
    k = 0.8 - 1.6 – 1
    k = -1.8
    Therefore, the vertex is (0.8 , -1.8)
    parallel
    General
    Maths-

    To identify the y-intercept of quadratic function, would you choose to use vertex form or standard form? Explain

    For identifying the y- intercept we have to put the value of x as 0 in the given function so that we can obtain the y-intercept
    If we see the standard form, we get an constant number c on putting the value of x=0. This value of c is called as y-intercept.
    But in vertex form it is not so easy to get y-intercept because in this form the constant term is not distinct as in the standard form
    So, Standard form is the right choice for identifying the y-intercept of quadratic function.

    To identify the y-intercept of quadratic function, would you choose to use vertex form or standard form? Explain

    Maths-General
    For identifying the y- intercept we have to put the value of x as 0 in the given function so that we can obtain the y-intercept
    If we see the standard form, we get an constant number c on putting the value of x=0. This value of c is called as y-intercept.
    But in vertex form it is not so easy to get y-intercept because in this form the constant term is not distinct as in the standard form
    So, Standard form is the right choice for identifying the y-intercept of quadratic function.
    General
    Maths-

    A water balloon is tossed into the air. The function h(x) = -0.5(x-4)2 + 9 gives the height, in feet, of the balloon from the surface of a pool as a function of the balloon’s horizontal distance from where it was first tossed. Will the balloon hit the ceiling 12 ft above the pool? Explain

    We have given a function of water balloon tossed into air,
    h(x) = -0.5(x-4)2 + 9
    The given equation is in the vertex form
    We know vertex is the point at maximum height .
    And y coordinate of vertex is the maximum height of the ball
    On comparing with the vertex form we get that
    h = 4
    k = 9
    Therefore, here vertex is (4, 9)
    Here, we have y-coordinate as 9
    So, the maximum height of ball is 9
    We have given the ceiling height as 12 ft
    So the height of ceiling is more than maximum height of ball , so ball will not hit the ceiling.

    A water balloon is tossed into the air. The function h(x) = -0.5(x-4)2 + 9 gives the height, in feet, of the balloon from the surface of a pool as a function of the balloon’s horizontal distance from where it was first tossed. Will the balloon hit the ceiling 12 ft above the pool? Explain

    Maths-General
    We have given a function of water balloon tossed into air,
    h(x) = -0.5(x-4)2 + 9
    The given equation is in the vertex form
    We know vertex is the point at maximum height .
    And y coordinate of vertex is the maximum height of the ball
    On comparing with the vertex form we get that
    h = 4
    k = 9
    Therefore, here vertex is (4, 9)
    Here, we have y-coordinate as 9
    So, the maximum height of ball is 9
    We have given the ceiling height as 12 ft
    So the height of ceiling is more than maximum height of ball , so ball will not hit the ceiling.
    General
    Maths-

    Sage began graphing f(x) = -2x2 + 4x + 9 by finding the axis of symmetry x = -1. Explain the error Sage made?

    We have given the equation f(x) = -2x2 + 4x + 9
    We will first find the axis of symmetry ‘

    x = -b/ 2a

         x = -4 / 2 (-2)

    x = -4/ -4

                                                                                x = 1
    This detects the error made by sage that he finds axis of symmetry as x = -1

    Sage began graphing f(x) = -2x2 + 4x + 9 by finding the axis of symmetry x = -1. Explain the error Sage made?

    Maths-General
    We have given the equation f(x) = -2x2 + 4x + 9
    We will first find the axis of symmetry ‘

    x = -b/ 2a

         x = -4 / 2 (-2)

    x = -4/ -4

                                                                                x = 1
    This detects the error made by sage that he finds axis of symmetry as x = -1

    parallel
    General
    Maths-

    How are the form and graph of f(x) = ax2 + bx + c similar to the form and graph of g(x) = ax2 + bx? How are they different?

    We have given the two functions
    f(x) = ax2 + bx + c
    g(x) = ax2 + bx
    By analyzing both the equations we get that both the equation are of same format
    In first equation the constant c is present whereas in second equation constant c is zero. So we know that in the standard form this constant represents the y- intercept of the curve.
    So the first curve intercepts y axis at (0,c)
    And second curve intercepts y axis at (0,0)

    How are the form and graph of f(x) = ax2 + bx + c similar to the form and graph of g(x) = ax2 + bx? How are they different?

    Maths-General
    We have given the two functions
    f(x) = ax2 + bx + c
    g(x) = ax2 + bx
    By analyzing both the equations we get that both the equation are of same format
    In first equation the constant c is present whereas in second equation constant c is zero. So we know that in the standard form this constant represents the y- intercept of the curve.
    So the first curve intercepts y axis at (0,c)
    And second curve intercepts y axis at (0,0)
    General
    Maths-

    How is the standard form of a quadratic function different from vertex form?

    Solution :- The standard quadratic form is ax2+bx+c=y, the vertex form of a quadratic equation is y=a(x−h)2+k.
    In both forms, y is the y-coordinate, x is the x-coordinate, and a is the constant that tells you whether the parabola is facing up (+a) or down (−a).It is as if the parabola was a bowl of applesauce; if there's a +a, I can add applesauce to the bowl; if there's a −a, I can shake the applesauce out of the bowl.
    The difference between a parabola's standard form and vertex form is that the vertex form of the equation also gives you the parabola's vertex: (h, k).

    How is the standard form of a quadratic function different from vertex form?

    Maths-General
    Solution :- The standard quadratic form is ax2+bx+c=y, the vertex form of a quadratic equation is y=a(x−h)2+k.
    In both forms, y is the y-coordinate, x is the x-coordinate, and a is the constant that tells you whether the parabola is facing up (+a) or down (−a).It is as if the parabola was a bowl of applesauce; if there's a +a, I can add applesauce to the bowl; if there's a −a, I can shake the applesauce out of the bowl.
    The difference between a parabola's standard form and vertex form is that the vertex form of the equation also gives you the parabola's vertex: (h, k).
    General
    Maths-

    Suppose the path of the ball in above figure is f(x) = -0.25(x-1)2 + 6.25. Find the ball’s initial and maximum heights.

    The given equation is f(x) = -0.25(x-1)2 + 6.25
    This is in the vertex form
    Therefore on comparing with the vertex form of a quadratic equation is y=a(x−h)2+k. we get,                                                                                 h = 1 , k = 6.25
    Therefore, vertex is (h,k) = (1, 6.25)
    So the maximum height of the ball is 6.25 .
    Converting the equation in standard form

    f(x) = -0.25(x-1)2 + 6.25

             f(x) = -0.25(x2+1 – 2x) + 6.25

                    f(x) = -0.25x2 – 0.25 + 0.5x + 6.25

         f(x) = -0.25x2 +0.5 x + 6.00
    Therefore, y intercept is c = 6
    Which is the initial height of the ball i.e 6

    Suppose the path of the ball in above figure is f(x) = -0.25(x-1)2 + 6.25. Find the ball’s initial and maximum heights.

    Maths-General
    The given equation is f(x) = -0.25(x-1)2 + 6.25
    This is in the vertex form
    Therefore on comparing with the vertex form of a quadratic equation is y=a(x−h)2+k. we get,                                                                                 h = 1 , k = 6.25
    Therefore, vertex is (h,k) = (1, 6.25)
    So the maximum height of the ball is 6.25 .
    Converting the equation in standard form

    f(x) = -0.25(x-1)2 + 6.25

             f(x) = -0.25(x2+1 – 2x) + 6.25

                    f(x) = -0.25x2 – 0.25 + 0.5x + 6.25

         f(x) = -0.25x2 +0.5 x + 6.00
    Therefore, y intercept is c = 6
    Which is the initial height of the ball i.e 6

    parallel
    General
    Maths-

    Mia tosses a a ball to her dog. The function -0.5(x-2)2 + 8 represents the ball path.

    1.What does the vertex form of the function tell you about the situation?
    Solution:- The standard quadratic form is ax2+bx+c=y, the vertex form of a quadratic equation is y=a(x−h)2+k.
    In both forms, y is the y-coordinate, x is the x-coordinate, and a is the constant that tells you whether the parabola is facing up (+a) or down (−a).
    The vertex form of the equation also gives you the parabola's vertex: (h,k).
    This vertex is the highest point on the trajectory of the ball tossed by mia.
    2.What does the standard form of a function tell you about the situation?
    Solution:- The standard quadratic form is ax2+bx+c=y
    In this the term c gives us the y-intercept of the curve
    In the given case it gives the height from which the ball is thrown.

    -0.5(x-2)2 + 8 = y

    - 0.5( x2+ 4 – 4x) + 8 = y

    -0.5x2 – 2 + 2x + 8 = y

    -0.5x2 + 2x + 6 = y

    C = 6
    Which is height from which the ball is thrown.

    Mia tosses a a ball to her dog. The function -0.5(x-2)2 + 8 represents the ball path.

    Maths-General
    1.What does the vertex form of the function tell you about the situation?
    Solution:- The standard quadratic form is ax2+bx+c=y, the vertex form of a quadratic equation is y=a(x−h)2+k.
    In both forms, y is the y-coordinate, x is the x-coordinate, and a is the constant that tells you whether the parabola is facing up (+a) or down (−a).
    The vertex form of the equation also gives you the parabola's vertex: (h,k).
    This vertex is the highest point on the trajectory of the ball tossed by mia.
    2.What does the standard form of a function tell you about the situation?
    Solution:- The standard quadratic form is ax2+bx+c=y
    In this the term c gives us the y-intercept of the curve
    In the given case it gives the height from which the ball is thrown.

    -0.5(x-2)2 + 8 = y

    - 0.5( x2+ 4 – 4x) + 8 = y

    -0.5x2 – 2 + 2x + 8 = y

    -0.5x2 + 2x + 6 = y

    C = 6
    Which is height from which the ball is thrown.

    General
    Maths-

    The trajectory of the water from Fountain A is represented by a function in standard form while the trajectory of the water from Fountain B is represented by table of values. Compare the vertex of each function. Which trajectory reached greatest height in feet?