Maths-

General

Easy

Question

# Find the axis of symmetry, vertex and y-intercept of the function

f(x) = 5x^{2} + 5x + 12

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.

Solution : -

## The correct answer is: 12

### 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)= 5x^{2} + 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)= 5x^{2} + 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.

The equation of the axis of symmetry for f(x)= 5x

^{2}+ 5x + 12 is x = -0.5.

The x coordinate of the vertex is the same:

The y coordinate of the vertex is :

^{2}+ 5h + 12

^{2}+ 5(-0.5) + 12

Therefore, the vertex is (-0.5 , 10.75)

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

^{2}+ 5(0) + 12

Therefore, Axis of symmetry is x = -0.5

Vertex is ( -0.5 , 10.75)

Y- intercept is 12.

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