How do you find f(2) if f(x) = 3x^2 – 2?
Understand the Problem
The question is asking you to evaluate the function f(x) = 3x^2 - 2 at x = 2. This means you need to substitute 2 for x in the expression and simplify to find the value of f(2).
Answer
$f(2) = 10$
Answer for screen readers
$f(2) = 10$
Steps to Solve
- Substitute $x$ with 2 in the function
Replace every instance of $x$ in the expression $3x^2 - 2$ with the number 2. This gives us $3(2)^2 - 2$.
- Evaluate the exponent
Calculate $2^2$, which is $2 * 2 = 4$. So the expression becomes $3(4) - 2$.
- Perform the multiplication
Multiply 3 by 4, which equals 12. Now the expression is $12 - 2$.
- Perform the subtraction
Subtract 2 from 12, which equals 10. Therefore, $f(2) = 10$.
$f(2) = 10$
More Information
The function $f(x) = 3x^2 - 2$ is a parabola. Evaluating the function at $x = 2$ gives the $y$-value of the parabola at that specific $x$-value.
Tips
A common mistake is to perform the operations in the wrong order. Remember to follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). In this case, the exponent should be evaluated before multiplication and subtraction.
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