CPM Homework Help : A2C Problem 8-7

Method 1:

Use the $x$ -intercepts.

Step 1 (method 1):

Notice that $\left(0, 0\right)$ and $\left(6, 0\right)$ are $x$ -intercepts.
What are the factors?

Step 2 (method 1):

The equation is $y = ax\left(x − 6\right)$ .
Substitute $\left(3, 9\right)$ into the equation and solve for a.

Method 2:

Use the vertex.

Step 1 (method 2):

Notice that since $3$ is midway between $0$ and $6$ , $\left(3, 9\right)$ is the vertex.
Write the equation in vertex form.

Step 2 (method 2):

The equation is
$y = a\left(x − 3\right)² + 9$ .
Substitute one of the
$x$ -intercepts into the equation and solve for $a$ .

Method 3:

Standard form.

Step 1 (method 3):

Substitute the three points into the equation
$y = ax² + bx + c$ to make a system of equations in three variables.

Step 2 (method 3):

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.