### Home > INT3 > Chapter 11 > Lesson 11.2.4 > Problem11-101

11-101.

What is the equation of the parabola that passes through the points $\left(–1, 10\right), \left(0, 5\right)$, and $\left(2, 7\right)$?

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

$a − b + c = 10$
$c = 5$
$4a + 2b + c = 7$

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.

$y = 2x^{2} − 3x + 5$

Use the eTool below to check your solution graphically.
Click the link at right for the full version of the eTool: INT3 11-101 HW eTool