Question

the equation $y = x^2 + 1$ represents a funct
use the function rule to complete
the table.
input ($x$) output ($y$)
$-2$ $5$
$-1$
$0$ ?
$1$ ?
$2$ ?

Explanation:

Step1: For \( x = -1 \)

Substitute \( x = -1 \) into \( y = x^2 + 1 \). We know that \( (-1)^2 = 1 \), so \( y = 1 + 1 = 2 \).

Step2: For \( x = 0 \)

Substitute \( x = 0 \) into \( y = x^2 + 1 \). Since \( 0^2 = 0 \), then \( y = 0 + 1 = 1 \).

Step3: For \( x = 1 \)

Substitute \( x = 1 \) into \( y = x^2 + 1 \). As \( 1^2 = 1 \), we get \( y = 1 + 1 = 2 \).

Step4: For \( x = 2 \)

Substitute \( x = 2 \) into \( y = x^2 + 1 \). We have \( 2^2 = 4 \), so \( y = 4 + 1 = 5 \).

Answer:

For \( x = -1 \), \( y = 2 \); for \( x = 0 \), \( y = 1 \); for \( x = 1 \), \( y = 2 \); for \( x = 2 \), \( y = 5 \). So the completed table (filling the blanks) is:

Input (\( x \))	Output (\( y \))
-1	2
0	1
1	2
2	5