### Home > AC > Chapter 12 > Lesson 12.4.1 > Problem12-71

12-71.

Find all of the points at which the parabolas below intersect. Write your solution(s) in $(x, y)$ form.

$y = x^2 − x + 12$
$y = 2x^2 + 3x + 7$

Set the equations equal to each other.

$x^² − x + 12 = 2x^² + 3x + 7$

Set the equation equal to zero.

$0 = x^² + 4x − 5$

Factor the expression.

Solve for $x$.

Substitute your answer for $x$ back into the equation and
solve for $y$ to find the points of intersection.