Question

Which of the following equations could represent the above graph?

• A. $f\left(x\right)=$ $(x-2{)}^2$
• B. $f\left(x\right)=$ $x^2-4$
• C. $f\left(x\right)=$ $4-x^2$
• D. $f\left(x\right)=$ $\left|\begin{array}{c}{x}^2-4\end{array}\right|$
• E. $f\left(x\right)=-$ $\left|\begin{array}{c}{x}^2-4\end{array}\right|$

Answer 1

The correct option is E $f\left(x\right)=-$ $\left|\begin{array}{c}{x}^2-4\end{array}\right|$

1. At $x=2,-2$ , the value of $y$ should be zero.
2. For $x<-2$ and $0<x<2$ , the value of $y$ should be increasing.
3. For $-2<x<0$ and $x>2$ , the value of $y$ should be decreasing.

The equation which satisfies these $3$ points is our required answer.

So, the correct option is $E$.