Q. 5 - Precalculus Enhanced with Graphing Utilities

Question

Find a so that the point $\left(-1, 2\right)$ is on the graph of $f\left(x\right)=a{x}^2+4$. 

Step-by-Step Solution

Answer

The value of a is $-2$.

Step 1. Given information

The given function is

$f\left(x\right)=a{x}^2+4$

Need to find the value of $a$ so that the point $\left(-1, 2\right)$ is on the graph.

Step 2. Solving for the value of a

Substitute $x=-1$ and $f\left(x\right)=2$ in the equation$f\left(x\right)=a{x}^2+4$,

$\begin{array}{rcl}2& =& a{\left(-1\right)}^2+4\\ 2& =& a\left(1\right)+4\\ a& =& 2-4\\ & =& -2\end{array}$

The value of a is $-2$.