Maths-

General

Easy

Question

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

f(x) = 2x^{2} + 8x + 2

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: 2

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

The equation of the axis of symmetry for f(x)= 2x

^{2}+ 8x + 2 is x = -2.

The x coordinate of the vertex is the same:

The y coordinate of the vertex is :

^{2}+ 8(h) + 2

^{2}+ 8(-2) + 2

Therefore, the vertex is (-2 , -6)

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

^{2}+ 8(0) + 2

Therefore, Axis of symmetry is x = -2

Vertex is ( -2 , -6)

Y- intercept is 2.