Chapter 8.5, Problem 100E

To determine

The system of two quadratic equations in which the graphs intersect at the given points.

Answer to Problem 100E

The equations are

  $\begin{array}{l}y=x^2+2x-8\\ y=-x^2-2x+8\end{array}$

Explanation of Solution

Given information:

A system of two quadratic equations whose graphs intersect at the given as shown below,

  $\left(-4,0\right)\text{and }\left(2,0\right)$

Formula used:

  $y=a\left(x-p\right)\left(x-q\right)$

Calculation:

Intercept form:

  $y=a\left(x-p\right)\left(x-q\right)$

Substitute the intercepts & simplify:

  $\begin{array}{l}y=a\left(x-\left(-4\right)\right)\left(x-2\right)\\ y=a\left(x+4\right)\left(x-2\right)\\ y=a\left(x^2+2x-8\right)\end{array}$

To find 2 equations let a be any constant value

Other than 0 (a = -1, 1):

  $\begin{array}{l}y=x^2+2x-8\\ y=-x^2-2x+8\end{array}$

Conclusion:

The equations are

  $\begin{array}{l}y=x^2+2x-8\\ y=-x^2-2x+8\end{array}$