Question

graph the function $f(x) = 4(x + 6)^2 + 4$. 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. graph with x-axis from -10 to 10 and y-axis (f(x)) from -10 to 10, grid lines present

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 $f(x)=4(x+6)^2+4$, rewrite $x+6$ as $x-(-6)$, so $h=-6$, $k=4$.

Step2: Locate the vertex

Vertex is $(-6, 4)$. Plot this point on the grid.

Step3: Find a second point

Choose $x=-5$ (1 unit right of vertex). Substitute into the function:
$f(-5)=4(-5+6)^2+4=4(1)^2+4=4+4=8$.
So the point is $(-5, 8)$.

Answer:

1. Vertex to plot: $(-6, 4)$
2. Second point to plot: $(-5, 8)$

(Connect these points and reflect over the vertical line $x=-6$ to draw the parabola)