### Home > AC > Chapter 11 > Lesson 11.3.1 > Problem 11-103

11-103.

Find all of the points at which the parabolas below intersect. Write your solution(s) in (*x*, *y*) form. 11-103 HW eTool (Desmos).** **Homework Help ✎

*y* = *x*^{2} + 5*x* − 4

*y* = *x*^{2} + *x* − 12

Set the equations equal to each other using the Equal Values Method.

Subtract *x*^{2} from both sides.

Subtract *x* from both sides.

Add 4 to both sides.

Divide by 4 on both sides.

Substitute the *x*-value you found into one of the original equations.

*x*^{2} + *x* − 12 = *x*^{2} + 5*x* − 4

*x* − 12 = 5*x* − 4

−12 = 4*x* − 4

−8 = 4*x*

−2 = *x*

*y* = (−2)^{2} + 5(−2) − 4*y* = 4 − 10 − 4*y* = −10

They intersect at (−2, −10)