Question

Which of the following graphs represents the equation below? f(x) = x^2 + 4x

Answer 1

Answer: Edmentum

Explanation:

Answer 2

The graph in the attached figure

Explanation:

we have

`f(x)=x^(2)+4x`

This is a vertical parabola open upward

The vertex is a minimum

step 1

Find the x-intercepts

The x-intercepts are the values of x when the value of the function is equal to zero

For f(x)=0

`0=x^(2)+4x`

Factor x

`0=x(x+4)`

The x-intercepts are (0,0) and (-4,0)

step 2

Find the y-intercept

The y-intercept is the values of the function when the value of x is equal to zero

For x=0

`f(x)=(0)^(2)+4(0)=0`

The y-intercept is (0,0)

step 3

Find the vertex

Convert the equation into vertex form

`f(x)=x^(2)+4x`

Complete the square

`f(x)=(x^(2)+4x+4)-4`

Rewrite as perfect squares

`f(x)=(x+2)^(2)-4`

The vertex is the point (-2,-4)

therefore

using a graphing a graphing tool

The graph in the attached figure