Question

graph the function $f(x) = -5(x - 5)^2$. 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.

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 $f(x)=-5(x-5)^2$, $h=5$, $k=0$.

Step2: Find vertex coordinates

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

Step3: Choose x-value, compute f(x)

Pick $x=4$:
$f(4)=-5(4-5)^2=-5(-1)^2=-5(1)=-5$
So the point is $(4, -5)$.

Step4: Choose another x-value, compute f(x)

Pick $x=6$:
$f(6)=-5(6-5)^2=-5(1)^2=-5(1)=-5$
So the point is $(6, -5)$.

Answer:

1. Plot the vertex at $\boldsymbol{(5, 0)}$
2. Plot a second point such as $\boldsymbol{(4, -5)}$ or $\boldsymbol{(6, -5)}$, then draw a downward-opening parabola through these points.