Answer :
To solve the problem of finding [tex]\( f(-4) \)[/tex] for the function [tex]\( f(x) = 3x^2 - 4 \)[/tex], follow these steps:
1. Understand the function: [tex]\( f(x) = 3x^2 - 4 \)[/tex] is a quadratic function.
2. Substitute the given value into the function: We need to evaluate the function at [tex]\( x = -4 \)[/tex].
3. Perform the calculation:
- Substitute [tex]\(-4\)[/tex] into the function: [tex]\( f(-4) = 3(-4)^2 - 4 \)[/tex].
- First, calculate [tex]\((-4)^2\)[/tex], which is [tex]\(16\)[/tex].
- Multiply [tex]\(16\)[/tex] by [tex]\(3\)[/tex]: [tex]\(3 \times 16 = 48\)[/tex].
- Subtract [tex]\(4\)[/tex] from [tex]\(48\)[/tex]: [tex]\(48 - 4 = 44\)[/tex].
4. Result: Therefore, [tex]\( f(-4) = 44 \)[/tex].
So, the correct answer is [tex]\( 44 \)[/tex].
1. Understand the function: [tex]\( f(x) = 3x^2 - 4 \)[/tex] is a quadratic function.
2. Substitute the given value into the function: We need to evaluate the function at [tex]\( x = -4 \)[/tex].
3. Perform the calculation:
- Substitute [tex]\(-4\)[/tex] into the function: [tex]\( f(-4) = 3(-4)^2 - 4 \)[/tex].
- First, calculate [tex]\((-4)^2\)[/tex], which is [tex]\(16\)[/tex].
- Multiply [tex]\(16\)[/tex] by [tex]\(3\)[/tex]: [tex]\(3 \times 16 = 48\)[/tex].
- Subtract [tex]\(4\)[/tex] from [tex]\(48\)[/tex]: [tex]\(48 - 4 = 44\)[/tex].
4. Result: Therefore, [tex]\( f(-4) = 44 \)[/tex].
So, the correct answer is [tex]\( 44 \)[/tex].
