Write the equation of the Quadratic Function in Vertex Form given the following three points on the parabola, (2,0) (3,2) (4,0).

Question

Please write the answer in vertex form.

Answer 1

Points (2,0) and (4,0) are x-intercept or zeros.

So f(x) = a(x - 2)(x - 4) is quadratic function in factored form. To get a we use point (3,2), f(3) = 2;

f(3) = a(3 - 2)(3 - 4) = 2; a = - 2.

f(x) = - 2(x - 2)(x - 4); f(x) = - 2x² + 12x -16.