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# Graph f(x) = 0.25x^{2} – 0.5x - 6. 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: -6

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)= 0.25x^{2} – 0.5x - 6, a= 0.25, b= -0.5, and c= -6. So, the equation for the axis of symmetry is given by

x = −(-0.5)/2(0.25)

x = 0.5/0.5

x = 1

The equation of the axis of symmetry for f(x)= = 0.25x^{2} – 0.5x - 6 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 = 0.25(h)^{2} – 0.5(h) - 6

k = 0.25(1)^{2} – 0.5(1) - 6

k = 0.25 – 0.5 – 6

k = -6.25

Therefore, the vertex is (1 , -6.25)

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

y = 0.25(0)^{2} – 0.5(0) - 6

y = 0 - 0 - 6

y = -6

Therefore, Axis of symmetry is x = 1

Vertex is ( 1 , -6.25)

Y- intercept is -6.

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