f(x)=|x+4| f(x) = -2x^2 - 3x+8

Question

Hi,

I have the problem f(x)=|x+4| f(x) = -2x²-3x+8. While I understand the basic concept on what's being solved for, I don't understand how to do so.

 

Could someone please explain this to me?

 

Thanks,

-Gabe

Answer 1

Since the first function is an absolute value, there are two solutions.

One is when the value of (x+4) is positive so |x+4| = (x+4). True when x >= -4.

The other is when (x+4) is negative so |x+4| = -(x+4). True when x <= -4.

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Equate the two functions and solve for each case. The domain of each case is limited!

Case 1: x >= -4:

-2x^2-3x+8 = x+4

-2x^2-4x+4 = 0

Solutions: -1+√(3), 1-√(3)

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Case 2: x <= -4

-2x^2-3x+8 = -(x+4)

-2x^2-2x+12 = 0

Solutions: -3, 2

The solutions are outside the domain where this equation is valid.

(If you plug these values for x into the original functions, you get the same magnitudes, but opposite signs.)