# Calculate the coordinates of the intersection points of the graphs of the function y = 3x ^ 2-15x and y = 0.

ax ^ 2 + bx + c = 0. This is exactly the form the quadratic equation has. The letters a, b, and c can be any real number, but a must never be zero.

Before x ^ 2 there is a coefficient a, which in our equation is equal to:

a = 3.

Before x is the coefficient b, which in our equation is:

b = -15.

Without x, this is the coefficient c, which our equation has:

c = 0.

The discriminant is a number equal to b ^ 2 – 4ac: D = b ^ 2 – 4ac = -15 ^ 2 – 4 * 3 * 0 = 225.

We are always looking for the discriminant to know the number of roots of a quadratic equation. If D <0, then there are no roots. If D = 0, then one root. If D> 0, then there are two roots. In our case:

D> 0, so there will be two roots: x = (-b ± D ^ (1/2)) / (2a).

D ^ (1/2) = 15.

x1 = (15 + 15) / (2 * 3) = 5.

x2 = (15 – 15) / (2 * 3) = 0.

Answer: 5, 0.