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Question

# Graph f(x) = -0.5x^{2} + 2x + 3. What are axis of symmetry, vertex and y-intercept of the function

Hint:

### For a quadratic function is in standard form, f(x)=ax2+bx+c.

A vertical line passing through the vertex is called the axis of symmetry for the parabola.

Axis of symmetry x=−b/2a

Vertex The vertex of the parabola is located at a pair of coordinates which we will call (*h, k*). where h is value of x in axis of symmetry formula and k is f(h).

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: 3

** **

This quadratic function is in standard form, f(x)=ax^{2}+bx+c.

For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.

In f(x)= = -0.5x^{2} + 2x + 3, a= -0.5, b=2, and c= 3. So, the equation for the axis of symmetry is given by

x = −(2)/2(-0.5)

x = -2/-1

x = 2

The equation of the axis of symmetry for f(x)= = -0.5x^{2} + 2x + 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 = -0.5(h)^{2} + 2(h) + 3

k = -0.5(2)^{2} + 2(2) + 3

k = -2 + 4 + 3

k = 5

Therefore, the vertex is (2 , 5)

For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

y = -0.5(0)^{2} + 2(0) + 3

y = 0 + 0 + 3

y = 3

Therefore, Axis of symmetry is x = 2

Vertex is ( 2 , 5)

Y- intercept is 3.

This quadratic function is in standard form, f(x)=ax

^{2}+bx+c.

For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.

In f(x)= = -0.5x

^{2}+ 2x + 3, a= -0.5, b=2, and c= 3. So, the equation for the axis of symmetry is given by

x = −(2)/2(-0.5)

x = -2/-1

x = 2

The equation of the axis of symmetry for f(x)= = -0.5x

^{2}+ 2x + 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 = -0.5(h)

^{2}+ 2(h) + 3

k = -0.5(2)

^{2}+ 2(2) + 3

k = -2 + 4 + 3

k = 5

Therefore, the vertex is (2 , 5)

For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

y = -0.5(0)

^{2}+ 2(0) + 3

y = 0 + 0 + 3

y = 3

Therefore, Axis of symmetry is x = 2

Vertex is ( 2 , 5)

Y- intercept is 3.

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