Find the Quadratic function y=a(x-h)^2 who's graph passes through the given points (4,-2) and (2,0)

Given:

The graph passes through the given points (4,-2) and (2,0).

To find:

The quadratic function .

Solution:

We have, quadratic function

           ...(i)

The graph passes through the given points (4,-2) and (2,0). It means the equation must be true for these points.

Putting x=4 and y=-2 in (i), we get

        ...(ii)

Putting x=2 and y=0 in (i), we get

         ...(iii)

Divide (iii) by (ii).

Putting h=2 in (ii), we get

Divide both sides by 4.

Putting and h=2 in (i), we get

Therefore, the required quadratic function is .