If you find an Absolute Value Quadratic, the same principle applies as in a linear equation: set up two equations (one positive and one negative).

Example

$$15 = |x^2 +7x|$$

You can create the two equations below:

$$15 = x^2 + 7x$$

$$-15 = x^2 + 7x$$

Set both equations to zero to get the more familiar quadratic form:

$$0 = x^2 +7x -15$$

$$0 = x^2 + 7x + 15$$

Why does it matter?

Now that we have two equations, we can find the total number of solutions using the Discriminant (see previous mountain entry). If both of the equations we created have positive discriminants, then it's possible for an absolute value quadratic to have $4$ solutions. Wow! Of course this is not guaranteed. It depends on the discriminant values. Or if we'd like we can try factoring both of the equations. It doesn't always work though.