To find the equation with a \( y \)-intercept value of 3, we need to evaluate the \( y \)-intercept of each given equation. The \( y \)-intercept of a function is found by setting \( x = 0 \) and solving for \( y \).
Let's examine each equation step-by-step:
### Equation A
[tex]\[ y = (x + 1)(x - 3) \][/tex]
Substitute \( x = 0 \):
[tex]\[ y = (0 + 1)(0 - 3) \][/tex]
[tex]\[ y = 1 \times (-3) \][/tex]
[tex]\[ y = -3 \][/tex]
The \( y \)-intercept for Equation A is -3.
### Equation B
[tex]\[ y = x^2 - 9 \][/tex]
Substitute \( x = 0 \):
[tex]\[ y = 0^2 - 9 \][/tex]
[tex]\[ y = -9 \][/tex]
The \( y \)-intercept for Equation B is -9.
### Equation C
[tex]\[ y = 3x(x - 3) \][/tex]
Substitute \( x = 0 \):
[tex]\[ y = 3 \times 0 \times (0 - 3) \][/tex]
[tex]\[ y = 0 \][/tex]
The \( y \)-intercept for Equation C is 0.
### Equation D
[tex]\[ y = (x + 1)(x + 3) \][/tex]
Substitute \( x = 0 \):
[tex]\[ y = (0 + 1)(0 + 3) \][/tex]
[tex]\[ y = 1 \times 3 \][/tex]
[tex]\[ y = 3 \][/tex]
The \( y \)-intercept for Equation D is 3.
Based on these calculations, the equation with a \( y \)-intercept value of 3 is:
[tex]\[ \boxed{D: y = (x + 1)(x + 3)} \][/tex]
