Question

$\text{For the function}f\left(x\right)=3x^2+2x-15,\text{find (a)}f\left(3\right)\text{(b)}f(-5)\text{(c)}f\left(0\right)\text{.}$

Short answer

The value of f(x) for each part is

ⓐ 18

ⓑ 50

ⓒ −15

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thegivenfunctionis}f\left(x\right)=3x^2+2x-15,\\ \text{Wehavetofind(a)}f\left(3\right)\text{(b)}f(-5)\text{(c)}f\left(0\right)\text{.}\end{array}$

Step 2. Substitute x=3 in fx

$\begin{array}{l}\text{Wehave}f\left(x\right)=3x^2+2x-15\\ \text{At}x=3,\text{wehave}\\ \Rightarrow f\left(3\right)=3{\left(3\right)}^2+2\left(3\right)-15\\ =3\left(9\right)+6-15\\ =27+6-15\\ =18\end{array}$

Step 3. Substitute x=−5 in fx

$\begin{array}{l}\text{Wehave}f\left(x\right)=3x^2+2x-15\\ \text{At}x=-5,\text{wehave}\\ \Rightarrow f(-5)=3{\left(-5\right)}^2+2\left(-5\right)-15\\ =3\left(25\right)-10-15\\ =75-10-15\\ =50\end{array}$

Step 4. Substitute x=0 in fx

$\begin{array}{l}\text{Wehave}f\left(x\right)=3x^2+2x-15\\ \text{At}x=0,\text{wehave}\\ \Rightarrow f\left(0\right)=3{\left(0\right)}^2+2\left(0\right)-15\\ =3\left(0\right)+0-15\\ =0+0-15\\ =-15\end{array}$