### Home > CCA2 > Chapter 7 > Lesson 7.1.1 > Problem7-7

7-7.

Find the equation of the parabola that passes through the points $(0,0),(3,9),\ \text{and}\ (6,0)$.

There are three ways to approach this problem.

Use the x-intercepts.

Notice that $(0,0)\ \text{and}\ (6,0)$ 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 $0\ \text{and}\ 6,(3,9)$ 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.