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

Step2: Left point 1 (x=-1)

Substitute $x=-1$ into $y=2x^2$:
$y=2(-1)^2=2(1)=2$. Point: $(-1,2)$

Step3: Left point 2 (x=-2)

Substitute $x=-2$ into $y=2x^2$:
$y=2(-2)^2=2(4)=8$. Point: $(-2,8)$

Step4: Right point 1 (x=1)

Substitute $x=1$ into $y=2x^2$:
$y=2(1)^2=2(1)=2$. Point: $(1,2)$

Step5: Right point 2 (x=2)

Substitute $x=2$ into $y=2x^2$:
$y=2(2)^2=2(4)=8$. Point: $(2,8)$

Answer:

Plot the points: $(0,0)$, $(-1,2)$, $(-2,8)$, $(1,2)$, $(2,8)$, then draw a smooth parabola through them.