### Home > A2C > Chapter 8 > Lesson 8.1.1 > Problem 8-7

Find the equation of the parabola that passes through the points (0, 0), (3, 9), and (6, 0). Homework Help ✎

There are three ways to approach this problem.

Use the *x*-intercepts.

Notice that (0, 0) and (6, 0) are *x*-intercepts.

What are the factors?

The equation is *y* = *ax*(*x* − 6).

Substitute (3, 9) into the equation and solve for *a*.

Use the vertex.

Notice that since 3 is midway between 0 and 6, (3, 9) is the vertex.

Write the equation in vertex form.

The equation is *y* = *a*(*x* − 3)² + 9.

Substitute one of the *x*-intercepts into the equation and solve for *a*.

Standard form.

Substitute the three points into the equation *y* = *ax*² + *bx* + *c* to make a system of equations in three variables.

Since you know what *c* is you can substitute it into all of the equations and solve a system of two equations in two variables.