Question

use the parabola tool to graph the quadratic function $f(x) = -5x^2 - 2$. graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Explanation:

Step1: Identify vertex form

Quadratic vertex form: $f(x)=a(x-h)^2+k$, vertex $(h,k)$
Rewrite given function: $f(x)=-5(x-0)^2-2$

Step2: Find vertex coordinates

From rewritten form, $h=0$, $k=-2$.
Vertex: $(0, -2)$

Step3: Find a second point

Choose $x=1$, substitute into $f(x)$:
$f(1)=-5(1)^2-2=-5-2=-7$
Second point: $(1, -7)$

Step4: Symmetric point (optional)

For $x=-1$, $f(-1)=-5(-1)^2-2=-7$, point $(-1, -7)$

Answer:

1. Plot the vertex at $(0, -2)$
2. Plot a second point at $(1, -7)$ (or $(-1, -7)$), then draw a downward-opening parabola passing through these points.