Question Given the function $$ f(x)=3 x^{2}+4 x-8 $$. Calculate the following values: $$ f(0)=\square $$ $$ f(2)=\square $$ $$ f(-2)=\square $$ $$ f(x+1)=\square $$ $$ f(-x)=\square $$ Question Help: Video D Post to forum Submit Question

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UpStudy AI · Accepted Answer

1. To compute $$ f(0) $$:
   $$
   f(0) = 3(0)^2 + 4(0) - 8 = 0 + 0 - 8 = -8.
   $$

2. To compute $$ f(2) $$:
   $$
   f(2) = 3(2)^2 + 4(2) - 8 = 3(4) + 8 - 8 = 12 + 8 - 8 = 12.
   $$

3. To compute $$ f(-2) $$:
   $$
   f(-2) = 3(-2)^2 + 4(-2) - 8 = 3(4) - 8 - 8 = 12 - 8 - 8 = -4.
   $$

4. To compute $$ f(x+1) $$, substitute $$ x+1 $$ into $$ f(x) $$:
   $$
   f(x+1) = 3(x+1)^2 + 4(x+1) - 8.
   $$
   First, expand $$(x+1)^2$$:
   $$
   (x+1)^2 = x^2 + 2x + 1.
   $$
   Then,
   $$
   f(x+1) = 3(x^2 + 2x + 1) + 4x + 4 - 8 = 3x^2 + 6x + 3 + 4x + 4 -8.
   $$
   Combine like terms:
   $$
   f(x+1) = 3x^2 + (6x + 4x) + (3 + 4 - 8) = 3x^2 + 10x - 1.
   $$

5. To compute $$ f(-x) $$, substitute $$-x$$ into $$ f(x) $$:
   $$
   f(-x) = 3(-x)^2 + 4(-x) -8.
   $$
   Since $$(-x)^2 = x^2$$,
   $$
   f(-x) = 3x^2 - 4x - 8.
   $$

Thus, the final values are:
- $$ f(0) = -8 $$
- $$ f(2) = 12 $$
- $$ f(-2) = -4 $$
- $$ f(x+1) = 3x^2 + 10x - 1 $$
- $$ f(-x) = 3x^2 - 4x - 8 $$
$$ f(0) = -8 $$, $$ f(2) = 12 $$, $$ f(-2) = -4 $$, $$ f(x+1) = 3x^2 + 10x - 1 $$, $$ f(-x) = 3x^2 - 4x - 8 $$.

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Given the function . Calculate the following values:

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