Question

graph the function $f(x) = 8(x + 2)^2$. plot the vertex. then plot another point on the parabola. if you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.

Explanation:

Step1: Identify vertex form

The function is in vertex form $f(x)=a(x-h)^2+k$, where $(h,k)$ is the vertex. For $f(x)=8(x+2)^2$, rewrite it as $f(x)=8(x-(-2))^2+0$.

Step2: Find the vertex

From the rewritten form, $h=-2$, $k=0$. So the vertex is $(-2, 0)$.

Step3: Calculate a second point

Choose $x=-1$. Substitute into the function:
$f(-1)=8(-1+2)^2=8(1)^2=8$.
This gives the point $(-1, 8)$.

Answer:

1. Vertex to plot: $(-2, 0)$
2. Second point to plot: $(-1, 8)$

(The parabola opens upwards, symmetric about the vertical line $x=-2$)