Chapter 8.1, Problem 23E

To determine

The function that includes the point $(-2,3)$ .

Answer to Problem 23E

The function $f(x)=a{x}^2$ includes the point $(-2,3)$ and $a=\frac{3}{4}$ .

Explanation of Solution

Given information: The functions $f(x)=a{x}^2(a>0),g(x)=a{x}^2(a<0)$ and the point $(-2,3)$

Calculation:

When $x<0$ , the functions $f(x)>0$ and $g(x)<0$

Consider the point $(-2,3)$

Here $x<0$ and $y>0$

So the function $f(x)=a{x}^2$ includes the point $(-2,3)$ .

Now put $x=-2,f(x)=3$

  $\begin{array}{l}$ 3=a{(-2)}^2$3=4a\\ a=\frac{3}{4}\end{array}$

Therefore the function $f(x)=a{x}^2$ includes the point $(-2,3)$ and $a=\frac{3}{4}$ .