CPM Homework Help : A2C Problem 7-72

Find the equation in $y=ax^2+bx+c$ form of the parabola that passes through the points $(1,5),(3,19),\ \text{and}\ (−2,29)$ .

Step 1:

Substitute the point $(1,5)$ into $y=ax^2+bx+c$ where $x=1$ and $y=5$ .

Step 2:

Repeat the previous step with $(3,19)$ and $(−2,29)$ to create two more equations.

Step 3:

You have created a system of three equations with three variables. Solve the system of equations.
Refer to problem 6-71 for help.

$a+b+c=5\\9a+3b+c=19\\4−2b+c=29$

Step 4:

$(a,b,c)=(3,−5,7)$ . Substitute for a, b, and c to find the equation of the parabola.

Use the eTool below to graph the answer.
Click the link at right for the full version of the eTool: 7-72 HW eTool