create the input-output table for the function f(x)=−(x+1)2+4. Which of the given x values produces the largest output for the function?

Question

x values:
-1
0
1
2

Answer 1

To create an input-output table for the function \( f(x) = - (x + 1)^2 + 4 \), we will calculate the output for each given \( x \) value.

Input-Output Table

| \( x \) | \( f(x) \) | |:---------:|:--------------:| | -1 | \( f(-1) = -((-1) + 1)^2 + 4 = -0 + 4 = 4 \) | | 0 | \( f(0) = -((0) + 1)^2 + 4 = -1 + 4 = 3 \) | | 1 | \( f(1) = -((1) + 1)^2 + 4 = -4 + 4 = 0 \) | | 2 | \( f(2) = -((2) + 1)^2 + 4 = -9 + 4 = -5 \) |

Summary of Outputs

• \( f(-1) = 4 \)
• \( f(0) = 3 \)
• \( f(1) = 0 \)
• \( f(2) = -5 \)

Largest Output

The largest output value from the given \( x \) values occurs at \( x = -1 \), where \( f(-1) = 4 \).