Question

How is the parabola graphed and what are the five points for the graph?

Answer 1

Given the parabola

$y=\frac{3}{4}x^2$

It is of the form

$y=ax^2$

and is symmetric to the y-axis and has vertex (0, 0).

To find two points on the left and right of the vertex, tae two points left and right of x = 0 and find the corresponding value of y.

When x = -1,

$y=\frac{3}{4}$

When x = -2,

$\begin{gathered} y=\frac{3}{4}\cdot(-2)^2 \\ =3 \end{gathered}$

Two points on the left of the vertex are (-1, 3/4) and (-2, 3).

When x = 1,

$y=\frac{3}{4}$

When x = 2,

$\begin{gathered} y=\frac{3}{4}\cdot2^2 \\ =3 \end{gathered}$

Two points on the right of the vertex are (1, 3/4) and (2, 3).

Plot the five points.