Question

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

Short answer

The value of a is $-2$.

Step-by-step solution

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 $-2$.