Question

1. find f(2) and f(a + h) when f(x) = 3x^2+2x + 4. (3 points)

Explanation:

Step1: Find f(2)

Substitute \(x = 2\) into \(f(x)=3x^{2}+2x + 4\).
\[

$$\begin{align*} f(2)&=3\times2^{2}+2\times2 + 4\\ &=3\times4+4 + 4\\ &=12 + 4+4\\ &=20 \end{align*}$$

\]

Step2: Find f(a + h)

Substitute \(x=a + h\) into \(f(x)=3x^{2}+2x + 4\).
\[

$$\begin{align*} f(a + h)&=3(a + h)^{2}+2(a + h)+4\\ &=3(a^{2}+2ah+h^{2})+2a + 2h+4\\ &=3a^{2}+6ah+3h^{2}+2a + 2h+4 \end{align*}$$

\]

Answer:

\(f(2)=20\), \(f(a + h)=3a^{2}+6ah+3h^{2}+2a + 2h+4\)