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Select the equation that has a [tex]$y$[/tex]-intercept value of 3.

A. [tex]y = (x + 1)(x - 3)[/tex]
B. [tex]y = x^2 - 9[/tex]
C. [tex]y = 3x(x - 3)[/tex]
D. [tex]y = (x + 1)(x + 3)[/tex]

Sagot :

GinnyAnswer
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]
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