How do you find the equation of a parabola given two x intercepts

Let's assume that the parabola has the following intersections with the x axis:

x1 = p

x2 = q

To find the equation of the parabola, we write the following product of binomials:

(x-p) (x-q) = 0

Where,

p, q: intersections with the x axis.

When developing the product of binomials, we obtain the equation of the parabola.

Answer:

(x-p) (x-q) = 0