Question

A parabola opening up or down has vertex of (0,0) and passes through (4,2). Write it’s equation in vertex form.

Answer 1

Given:

Given that a parabola opening up or down has vertex of (0,0) and passes through the point (4,2).

We need to determine the equation of parabola in vertex form.

Equation of the parabola:

The general form to write the equation of the parabola in vertex form is given by

`y=a(x-h)^2+k`

where (h,k) is the vertex and a is the constant.

Substituting the vertex (0,0) in the above form, we get;

`y=a(x-0)^2+0`

`y=ax^2` ------ (1)

Since, the parabola passes through the point (4,2), let us substitute the point in the above equation.

Thus, we have;

`2=a(4)^2`

`2=16a`

`(1)/(8)=a`

Thus, substituting
`a=(1)/(8)` in equation (1), we get;

`y=((1)/(8))x^2`

Thus, the equation of the parabola in vertex form is
`y=((1)/(8))x^2`