Question

graph the function $f(x) = -2(x - 5)^2$. 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 y-axis from -10 to 10, grid lines

Explanation:

Step1: Identify vertex form

The quadratic function is in vertex form $f(x)=a(x-h)^2+k$, where $(h,k)$ is the vertex. For $f(x)=-2(x-5)^2$, $h=5$, $k=0$.

Step2: Find the vertex

Vertex is $(h,k)=(5, 0)$.

Step3: Pick x-value, solve for f(x)

Choose $x=6$. Substitute into the function:
$f(6)=-2(6-5)^2=-2(1)^2=-2$
So the point is $(6, -2)$.

Step4: Confirm parabola direction

Since $a=-2<0$, the parabola opens downward.

Answer:

1. Plot the vertex at the coordinate $(5, 0)$.
2. Plot a second point at $(6, -2)$, then draw a downward-opening parabola symmetric about the vertical line $x=5$ passing through these points.