Find f ( − 3 ) f(- 3) for the following functions. (A) f ( x ) = 2 x 2 − 4 x + 1 f\left(x\right)=2x^2-4x+1

this problem, we're asked to find f of negative three for the following functions, and we'll start with example a. So finding f of negative three simply means that my input or x values are going to be replaced with negative three. So let's go ahead and do that. So we're trying to find f of negative three, which is going to be two times negative three squared minus four times negative three, then that's gonna be plus one. So from here, we can try to simplify this. Now negative three squared is gonna give me positive nine, so we'll have two times nine minus, and then we have four times negative three. Now four times negative three is gonna give us negative 12. But I noticed that that negative 12 is gonna cancel with the negative sign right there, so I'll have negative negative 12, which is the same thing as positive 12, then that's gonna be plus one. Now two times nine is 18. So we have 18 plus 12 plus one. Now 18 plus 12 is 30, plus one, that gives us 31. So f of negative three is 31, and that is the answer to this problem.

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Multiple Choice

Find $f of negative 3$ for the following functions.
(A) $f (x) = 2 x^{2} - 4 x + 1$

$31$

$29$

$34$

$25$

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Verified step by step guidance

Identify the function given: $f(x) = 2x^2 - 4x + 1$.

Substitute the value $x = -3$ into the function to find $f(-3)$, so write $f(-3) = 2(-3)^2 - 4(-3) + 1$.

Calculate the square of $-3$, which is $(-3)^2$, and rewrite the expression as $f(-3) = 2 \times 9 - 4(-3) + 1$.

Multiply the constants with the results of the powers and substitutions: \$2 \times 9$ and $-4 \times (-3)$, so the expression becomes $f(-3) = 18 + 12 + 1$.

Add all the terms together: \$18 + 12 + 1$ to get the value of $f(-3)$.

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Find f(−3)f(- 3) for the following functions.(A) f(x)=2x2−4x+1f\left(x\right)=2x^2-4x+1

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Find $f of negative 3$ for the following functions.
(A) $f (x) = 2 x^{2} - 4 x + 1$