Question

im2 midterm study guide #3
test overview 7
question 9
given $f(x) = 2x^2 - 6x - 12$, find $f(-9)$
answer
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Explanation:

Step1: Substitute \( x = -9 \) into \( f(x) \)

We have the function \( f(x) = 2x^2 - 6x - 12 \). To find \( f(-9) \), we replace every \( x \) in the function with \( -9 \). So we get \( f(-9)=2(-9)^2 - 6(-9)-12 \).

Step2: Calculate each term

First, calculate \( (-9)^2 \). We know that \( (-9)^2=(-9)\times(-9) = 81 \). Then, \( 2\times(-9)^2=2\times81 = 162 \). Next, calculate \( -6\times(-9)=54 \). Now our expression becomes \( 162 + 54-12 \).

Step3: Simplify the expression

Add \( 162 \) and \( 54 \) first: \( 162 + 54=216 \). Then subtract \( 12 \) from \( 216 \): \( 216-12 = 204 \).

Answer:

\( 204 \)