Question

graph the function $f(x) = -6(x + 5)^{2}$.
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.
graph with x-axis from -10 to 10 and f(x)-axis from -10 to 10, grid lines

Explanation:

Step1: Identify vertex form

The vertex form of a parabola is $f(x)=a(x-h)^2+k$, where $(h,k)$ is the vertex.
For $f(x)=-6(x+5)^2$, rewrite as $f(x)=-6(x-(-5))^2+0$.

Step2: Find the vertex

From the rewritten form, $h=-5$, $k=0$. So the vertex is $(-5, 0)$.

Step3: Calculate a second point

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

Answer:

1. Vertex to plot: $(-5, 0)$
2. Second point to plot: $(-4, -6)$

(The parabola opens downward, symmetric about the vertical line $x=-5$)