Question

Which of the following equations has a graph in the $xy$-plane for which $y$ is always greater than or equal to $-1$ ?

• A. $y=|x|-2$
• B. $y=x^2-2$
• C. $y=(x-2{)}^2$
• D. $y=x^3-2$

Answer 1

The correct option is C $y=(x-2{)}^2$

A. $y=|x|-2$

Since the minimum value of $|x|$ is $0$, the minimum value of $y$ becomes $-2$

B. $y=x^2-2$

Since the minimum value of $x^2$ is 0, the minimum value of $y$ becomes $-2$

C. $y=(x-2{)}^2$

Any square number is non-negative and so the minimum value of $y$ is zero.

D. $y=x^3-2$

$x^3$ can go upto negative infinity and so even $y$.