Question

determine the ( x )-intercepts of the following equation. ((-5x - 25)(4x + 16) = y) answer ( (-5,0) ) and ( (4,0) ) ( (-5,0) ) and ( (-4,0) ) ( (-400,0) ) ( (0,400) ) ( (0,-5) ) and ( (0,-4) ) ( (0,-400) )

Explanation:

Step1: Recall x-intercept definition

x-intercepts occur where \( y = 0 \). So set \( y = 0 \) in the equation \( (-5x - 25)(4x + 16)=y \), getting \( (-5x - 25)(4x + 16)=0 \).

Step2: Solve each factor

For a product to be zero, at least one factor is zero.

• Solve \( -5x - 25 = 0 \):

Add 25 to both sides: \( -5x = 25 \), divide by -5: \( x = -5 \).

• Solve \( 4x + 16 = 0 \):

Subtract 16: \( 4x = -16 \), divide by 4: \( x = -4 \).
So the x-intercepts are when \( x = -5 \) (y=0) and \( x = -4 \) (y=0), i.e., \( (-5, 0) \) and \( (-4, 0) \).

Answer:

\( (-5,0) \) and \( (-4,0) \)