Given the function $$ f $$, find $$ f(-2), f(-1), f(0), f(1) $$, and $$ f(2) $$. $$ f(x)=3 x^{2}-2 x+4 $$ $$ f(-2)=\square $$ $$ f(0)=\square $$ $$ f(1)=\square $$ $$ f(2)=\square $$

Question

UpStudy AI · Accepted Answer

We are given
$$
f(x)=3x^2-2x+4.
$$

**Step 1: Compute $$f(-2)$$**
$$
f(-2)=3(-2)^2-2(-2)+4.
$$
First, compute $$(-2)^2=4$$:
$$
3(4)=12.
$$
Then, $$-2(-2)=4$$. So,
$$
f(-2)=12+4+4=20.
$$

**Step 2: Compute $$f(-1)$$**
$$
f(-1)=3(-1)^2-2(-1)+4.
$$
Since $$(-1)^2=1$$:
$$
3(1)=3.
$$
And $$-2(-1)=2$$. Thus,
$$
f(-1)=3+2+4=9.
$$

**Step 3: Compute $$f(0)$$**
$$
f(0)=3(0)^2-2(0)+4.
$$
This simplifies to:
$$
f(0)=0+0+4=4.
$$

**Step 4: Compute $$f(1)$$**
$$
f(1)=3(1)^2-2(1)+4.
$$
Since $$1^2=1$$:
$$
3(1)=3.
$$
Then,
$$
f(1)=3-2+4=5.
$$

**Step 5: Compute $$f(2)$$**
$$
f(2)=3(2)^2-2(2)+4.
$$
Calculate $$(2)^2=4$$:
$$
3(4)=12.
$$
Then, $$-2(2)=-4$$. Hence,
$$
f(2)=12-4+4=12.
$$

The computed values are:
$$
\begin{aligned}
f(-2)&=20,\
f(-1)&=9,\
f(0)&=4,\
f(1)&=5,\
f(2)&=12.
\end{aligned}
$$
$$ \begin{aligned} f(-2) &= 20, \ f(-1) &= 9, \ f(0) &= 4, \ f(1) &= 5, \ f(2) &= 12. \end{aligned} $$

Given the function \( f \), find \( f(-2), f(-1), f(0), f(1) \), and \( f(2) \). \( f(x)=3 x^{2}-2 x+4 \) \( f(-2)=\square \) \( f(0)=\square \) \( f(1)=\square \) \( f(2)=\square \)

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