Question

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

Answer 1

Given the parabola

`y=(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=(3)/(4)`

When x = -2,

`\begin{gathered} y=(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=(3)/(4)`

When x = 2,

`\begin{gathered} y=(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.