By definition and properties of the absolute value used on the quadratic equation we conclude that F(|- 4|) = 12.
How to evaluate a quadratic equation with an absolute value
Herein we must apply the definition of absolute value prior to evaluating the quadratic equation defined in the statement. From algebra we know that absolute values are defined as:
|x| = x, when x ≥ 0 or - x, when x < 0. (1)
Then, we apply (1) on the quadratic equation:
F(|x|) = |x|² - 2 · |x| + 4
As x < 0, by absolute value properties:
F(|x|) = x² + 2 · x + 4
F(|- 4|) = (- 4)² + 2 · (- 4) + 4
F(|- 4|) = 16 - 8 + 4
F(|- 4|) = 12
By definition and properties of the absolute value used on the quadratic equation we conclude that F(|- 4|) = 12.
To learn more on absolute values: https://brainly.com/question/1301718
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