Maths-

General

Easy

Question

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

f(x) = 4x^{2} + 12x + 5

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: 5

### 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)= = 4x^{2} + 12x + 5, a= 4, b= 12, and c= 5. So, the equation for the axis of symmetry is given by

x = −(12)/2(4)

x = -12/8

x = -3/2 = -1.5

The equation of the axis of symmetry for f(x)= = 4x^{2} + 12x + 5 is x = -1.5.

The x coordinate of the vertex is the same:

h = -1.5

The y coordinate of the vertex is :

k = f(h)

k = 4h^{2} + 12h + 5

k = 4(-1.5)^{2} + 12(-1.5) + 5

k = 9 – 18 + 5

k = -4

Therefore, the vertex is (-1.5 , -4)

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

y = 4(0)^{2} + 12(0) + 5

y = 0 + 0 + 5

y = 5

Therefore, Axis of symmetry is x = -1.5

Vertex is ( -1.5 , -4)

Y- intercept is 5.

The equation of the axis of symmetry for f(x)= = 4x

^{2}+ 12x + 5 is x = -1.5.

The x coordinate of the vertex is the same:

The y coordinate of the vertex is :

^{2}+ 12h + 5

^{2}+ 12(-1.5) + 5

Therefore, the vertex is (-1.5 , -4)

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

^{2}+ 12(0) + 5

Therefore, Axis of symmetry is x = -1.5

Vertex is ( -1.5 , -4)

Y- intercept is 5.

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