Question
When \( f(x)=3 x^{2}+4 x+6 \), evaluate \( f(-3) \)
Ask by Graham Curry. in the United States
Dec 03,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f(-3) = 21 \)
Solution
Substitute \( x=-3 \) into the expression \( 3x^2+4x+6 \).
Evaluate the expression by following steps:
- step0: Evaluate:
\(3x^{2}+4x+6\)
- step1: Substitute:
\(3\left(-3\right)^{2}+4\left(-3\right)+6\)
- step2: Multiply the terms:
\(3^{3}+4\left(-3\right)+6\)
- step3: Multiply the numbers:
\(3^{3}-12+6\)
- step4: Evaluate the power:
\(27-12+6\)
- step5: Calculate:
\(21\)
When \( f(x)=3x^{2}+4x+6 \), evaluating \( f(-3) \) gives \( f(-3) = 21 \).
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Simplify this solution Extra Insights
To evaluate \( f(-3) \), we need to substitute \(-3\) into the function \( f(x) = 3x^2 + 4x + 6 \). So we calculate: \[ f(-3) = 3(-3)^2 + 4(-3) + 6 \] \[ = 3(9) - 12 + 6 \] \[ = 27 - 12 + 6 \] \[ = 27 - 6 \] \[ = 21 \] Thus, \( f(-3) = 21 \).
