Q. 84 - Precalculus Enhanced with Graphing Utilities

Question

If $f\left(x\right)=3x^2-Bx+4$ and $f(-1)=12$, what is the value of $B$?

Step-by-Step Solution

Answer

The value of $B=5$

Step 1. Given Information

If $f\left(x\right)=3x^2-Bx+4$ and $f(-1)=12$

We have to find the value of $B$.

Step 2. To find the value of B we firstly find the x = - 1 by putting in the given function.

$$\begin{gathered} f(-1)=3{(-1)}^2-B(-1)+4 \\ f(-1)=3·1+B+4 \\ f(-1)=3+B+4 \\ f(-1)=7+B \end{gathered}$$

Step 3. Now the function is f ( - 1 ) = 7 + B . We know f ( - 1 ) = 12 so we put the value of f ( - 1 ) in the function.

$12=7+B$

Subtract 7 on both side

$$\begin{gathered} 12-7=7+B-7 \\ 5=B \\ B=5 \end{gathered}$$