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;

$2=a(4)^2$

$2=16a$

$\frac{1}{8}=a$

Thus, substituting $a=\frac{1}{8}$ in equation (1), we get;

$y=(\frac{1}{8})x^2$

Thus, the equation of the parabola in vertex form is $y=(\frac{1}{8})x^2$