CPM Homework Help : A2C Problem 7-80

Find an equation for the parabola that passes through the points $(−1,10),(0,5),\ \text{and}\ (2,7)$ .

Step 1:

Create a system of three equations in three variables using the points and the equation $y=ax^2+bx+c$ .

$a−b+c=10\\c=5\\4a+2b+c=7$

Step 2:

Substitute the value for c into the first and third equations to simplify.
You now have a system of two equations with two variables to solve.

Answer:

$y=2x^2−3x+5$

Use the eTool below to check your solution graphically.
Click the link at right for the full version of the eTool: 7-80 HW eTool