Question

!PLEASE HELP ME!

Tim thinks that the following expression will only yield values that are positive. x^2

Is Tim correct? Explain why or why not and provide three examples that prove whether Tim’s statement is correct.

Answer 1

No, Tim is not correct. The expression
`x^2` can yield both positive and negative values depending on the value of x.

Step-by-step explanation:

No, Tim is not correct. The expression
`x^2` can yield both positive and negative values depending on the value of x. Here are three examples:

1. If x = 2, then
   `2^2` = 4, which is positive.
2. If x = -2, then
   `(-2)^2` = 4, which is also positive.
3. If x = 0, then
   `0^2` = 0, which is neither positive nor negative.

As you can see, the value of x can result in both positive and zero values for the expression
`x^2`, so Tim's statement is incorrect.

Answer 2

We conclude that Tim is correct when he says that the expression x² only yields values that are positive.

Step-by-step explanation:

Given the expression

x²

• Plug in and checking x = 1 and x = -1 in the expression

Putting x = 1 in the expression

x²= (1)² = 1

Putting x = -1 in the expression

x²= (-1)² = 1

Thus, the expression yields the same output '1' when we enter x = 1, and x=-1.

• Plug in and checking x = 2 and x = -2 in the expression

Putting x = 2 in the expression

x²= (2)² = 4

Putting x = -1 in the expression

x²= (-2)² = 4

Thus, the expression yields the same output '4' when we enter x = 2, and x=-2.

• Plug in and checking x = 3 and x = -3 in the expression

Putting x = 3 in the expression

x²= (3)² = 9

Putting x = -1 in the expression

x²= (-3)² = 9

Thus, the expression yields the same output '9' when we enter x = 3, and x=-3.

The reason why the expression x² only yields positive values because the expression is in the square form, and the square of any number will always yield a positive value, no matter whether the input number is negative or positive.

Therefore, we conclude that Tim is correct when he says that the expression x² only yields values that are positive.