Question

graph the function $f(x) = -5x^2$. 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: Find the vertex of the parabola

For a quadratic function in the form $f(x)=ax^2+bx+c$, when $b=0$, the vertex is at $(0, f(0))$.
$f(0) = -5(0)^2 = 0$, so the vertex is $(0,0)$.

Step2: Find a second point on the parabola

Choose $x=1$, substitute into the function:
$f(1) = -5(1)^2 = -5$, so the point is $(1,-5)$.
(We can also use $x=-1$: $f(-1) = -5(-1)^2 = -5$, giving $(-1,-5)$)

Step3: Determine parabola direction

Since $a=-5<0$, the parabola opens downward.

Answer:

1. Plot the vertex at $(0, 0)$.
2. Plot a second point at $(1, -5)$ (or $(-1, -5)$).
3. Draw a downward-opening parabola symmetric about the y-axis passing through these points.