Question

graph the parabola.

$y = 2x^{2}$

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 a parabola of the form $y = ax^{2}+bx + c$, in $y = 2x^{2}$, $a = 2$, $b=0$, $c = 0$. The x - coordinate of the vertex is $x=-\frac{b}{2a}=0$. Substituting $x = 0$ into $y = 2x^{2}$, we get $y=0$. So the vertex is $(0,0)$.

Step2: Find points to the left of the vertex

Let $x=-1$, then $y=2\times(-1)^{2}=2$. Let $x = - 2$, then $y=2\times(-2)^{2}=8$. The points are $(-1,2)$ and $(-2,8)$.

Step3: Find points to the right of the vertex

Let $x = 1$, then $y=2\times1^{2}=2$. Let $x=2$, then $y=2\times2^{2}=8$. The points are $(1,2)$ and $(2,8)$.

Answer:

The five points are $(0,0)$, $(-1,2)$, $(-2,8)$, $(1,2)$, $(2,8)$