Question

graph the parabola
$y = -3x^2$
plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. then click on the graph-a-function button.

Explanation:

Step1: Find the vertex

For $y = ax^2+bx+c$, vertex at $x=-\frac{b}{2a}$. Here $a=-3, b=0$, so $x=0$. Substitute $x=0$: $y=-3(0)^2=0$. Vertex: $(0,0)$

Step2: Pick left x-values, find y

Choose $x=-1, -2$.
For $x=-1$: $y=-3(-1)^2=-3$ → $(-1,-3)$
For $x=-2$: $y=-3(-2)^2=-12$ → $(-2,-12)$

Step3: Pick right x-values, find y

Choose $x=1, 2$.
For $x=1$: $y=-3(1)^2=-3$ → $(1,-3)$
For $x=2$: $y=-3(2)^2=-12$ → $(2,-12)$

Answer:

Five points to plot:

1. Vertex: $(0, 0)$
2. Left points: $(-1, -3)$, $(-2, -12)$
3. Right points: $(1, -3)$, $(2, -12)$

After plotting these points, click the "Graph-a-function" button to draw the downward-opening parabola.