Question

How do we plot the five points to graph the parabola?

Answer 1

Given: The equation below

$y=\frac{3}{2}x^2$

To Determine: The graph of the given equation by plotting 5 points

The vertex, two points to the left of the vertex, and two points to the right of the vertex

Let us find the vertex of the parabola

This can be found by

$\begin{gathered} x=-\frac{b}{2a} \\ y=\frac{3}{2}x^2,a=\frac{3}{2},b=0,c=0 \\ x=-\frac{0}{2\times\frac{3}{2}}=\frac{-0}{3}=0 \end{gathered}$

The x value of the vertex is, x = 0

Therefore two points to the left of the vertex would be

$x=-2,x=-1$

Two points to the right of the vertex would be

$x=1,x=2$

Let us find the corresponding values of y at this 5 points as shown in the table below

The graph of the points is as shown below

Hence, the above parabola is the required