Answer: h(x) = 8x so choice A.
Explanation:
f(x) = (x + 2)² - 1
g(x) = -(x - 2)² + 1
SOLVE:
h(x) = f(x) + g(x)
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Step 1: Put together
((x + 2)² - 1) + (-(x - 2)² + 1)
Step 2: Positive and Negative 1 add to 0
((x + 2)² - ) + (-(x - 2)² + )
Step 3: Rewrite
(x + 2)² - (x - 2)²
Step 3: Expand the expression
(x + 2)(x + 2) - (x - 2)(x - 2)
Step 4: Distribute
(x² + 4x + 4) - (x² - 4x + 4)
Step 5: Remove Parentheses (don't forget to distribute the negative)
x² + 4x + 4 - x² + 4x - 4
Step 6: Collect Like Terms
x² and -x² add to 0
+ 4 and - 4 add up to 0
Leaving only + 4x and + 4x which add up to 8x
Therefore, h(x) = f(x) + g(x), h(x) = 8x
Graph Letter A: