Find the equation of the parabola

Question

A parabola has an equation of the form y=ax²+bx+c. It passes through the points (0,3), (1,0), and (3,0). Find the equation of this parabola in the form y=a(x-h)²+k.

I don’t know the steps of how to solve this question, it would be nice if I could get some help, as I have a test on this topic as of tomorrow.

Answer 1

This quadratic function has two zeros x= 1 and x=3 (given by X-intercepts (1,0), and (3,0)).

So the equation is y = a(x-1)(x-3). Point (0,3)should satisfy this equation so a=1.

The vertex of any parabola is located in the midpoint between zeros at x = h = (3+1)/2 =2.

The vertex form of the equation is y = (x-2)² + k.

To find k plug point (0,3): 3 = (0-2)² + k, k = -1