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QuestionEvaluate the function h(x)=−x2h(x)=-x^{2} for: a. h(−8)h(-8), b. h(−12)h\left(-\frac{1}{2}\right), c. h(12)h\left(\frac{1}{2}\right).

Studdy Solution

STEP 1

Assumptions1. The function is defined as h(x)=−xh(x) = -x^{}

STEP 2

To find the indicated values, we need to substitute the given values into the function.
a. For h(−8)h(-8), we substitute −8-8 into the functionh(−8)=−(−8)2h(-8) = -(-8)^{2}

STEP 3

Calculate the value of h(−8)h(-8).
h(−8)=−(−8)2=−64h(-8) = -(-8)^{2} = -64

STEP 4

Now, for h(−12)h\left(-\frac{1}{2}\right), we substitute −12-\frac{1}{2} into the functionh(−12)=−(−12)2h\left(-\frac{1}{2}\right) = -\left(-\frac{1}{2}\right)^{2}

STEP 5

Calculate the value of h(−12)h\left(-\frac{1}{2}\right).
h(−12)=−(−12)2=−14h\left(-\frac{1}{2}\right) = -\left(-\frac{1}{2}\right)^{2} = -\frac{1}{4}

STEP 6

Finally, for h(12)h\left(\frac{1}{2}\right), we substitute 12\frac{1}{2} into the functionh(12)=−(12)2h\left(\frac{1}{2}\right) = -\left(\frac{1}{2}\right)^{2}

STEP 7

Calculate the value of h(12)h\left(\frac{1}{2}\right).
h(12)=−(12)2=−14h\left(\frac{1}{2}\right) = -\left(\frac{1}{2}\right)^{2} = -\frac{1}{4}So, the indicated values are h(−)=−64h(-) = -64, h(−12)=−14h\left(-\frac{1}{2}\right) = -\frac{1}{4}, and h(12)=−14h\left(\frac{1}{2}\right) = -\frac{1}{4}.

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