Question

y = 3x²
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 $x=-1, x=-2$.
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 $x=1, x=2$.
For $x=1$: $y=3(1)^2=3$ → $(1,3)$
For $x=2$: $y=3(2)^2=12$ → $(2,12)$

Answer:

The five points are:
Vertex: $(0, 0)$
Left points: $(-1, 3)$, $(-2, 12)$
Right points: $(1, 3)$, $(2, 12)$