Question

graph the function $f(x) = 6(x + 8)^2 - 7$. 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 $f(x)=6(x+8)^2-7$, rewrite as $f(x)=6(x-(-8))^2+(-7)$.

Step2: Find vertex coordinates

From the rewritten form, $h=-8$, $k=-7$.
Vertex: $(-8, -7)$

Step3: Find a second point

Choose $x=-7$ (1 unit right of vertex).
Substitute $x=-7$ into $f(x)$:
$f(-7)=6(-7+8)^2-7=6(1)^2-7=6-7=-1$
Second point: $(-7, -1)$

Step4: Symmetric point (optional)

For $x=-9$ (1 unit left of vertex):
$f(-9)=6(-9+8)^2-7=6(1)^2-7=-1$
Symmetric point: $(-9, -1)$

Answer:

1. Vertex to plot: $(-8, -7)$
2. Second point to plot: $(-7, -1)$ (or $(-9, -1)$)

The parabola opens upward (since $a=6>0$) with these points defining its shape.