CPM Homework Help : INT3 Problem 11-108

Write the equation in standard form of the parabola that passes through the points $\left(1, 5\right), \left(3, 19\right)$ , and $\left(–2, 29\right)$ .

Step 1:

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

Step 2:

Repeat the previous step with $\left(3, 19\right)$ and $\left(−2, 29\right)$ 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 11-100 for help.

$a + b + c = 5$
$9a + 3b + c = 19$
$4 − 2b + c = 29$

Step 4:

$\left(a, b, c\right) = \left(3, −5, 7\right)$ . 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: INT3 11-108 HW eTool