Question

determine the ( x )-intercepts of the following equation.

( (x + 4)(x + 1) = y )

answer

( (0, -4) ) and ( (0, -1) )
( (0, -4) )
( (-4, 0) ) and ( (1, 0) )
( (4, 0) )
( (-4, 0) ) and ( (-1, 0) )
( (0, 4) )

Explanation:

Step1: Recall x-intercept definition

x-intercepts occur where \( y = 0 \). So set \( y = 0 \) in the equation \( (x + 4)(x + 1)=y \).
$$(x + 4)(x + 1)=0$$

Step2: Solve for x using zero - product property

The zero - product property states that if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \).
For \( (x + 4)(x + 1)=0 \), we have two cases:

• Case 1: \( x+4 = 0 \)

Subtract 4 from both sides: \( x=-4 \)

• Case 2: \( x + 1=0 \)

Subtract 1 from both sides: \( x=-1 \)

When \( x=-4 \), \( y = 0 \), so the point is \( (-4,0) \). When \( x=-1 \), \( y = 0 \), so the point is \( (-1,0) \).

Answer:

\((-4,0)\) and \((-1,0)\)