CPM Homework Help : CCA2 Problem 7-7

Method 1:

Use the x-intercepts.

Step 1 Method 1:

Notice that $(0,0)\ \text{and}\ (6,0)$ are x-intercepts.
What are the factors?

Step 2 Method 1:

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

Method 2:

Use the vertex.

Step 1 Method 2:

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

Step 2 Method 2:

The equation is
$y=a(x−3)^2+9$ .
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
$y=ax^2+bx+c$ 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.