Question

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

Answer 1

Answer:

The graph in the attached figure

Step-by-step 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