Question

which function has only one x-intercept at (-6, 0)?
○ f(x) = x(x - 6)
○ f(x) = (x - 6)(x - 6)
○ f(x) = (x + 6)(x - 6)
○ f(x) = (x + 6)(x + 6)

Explanation:

Step1: Find roots of each function

Set $f(x)=0$ for each option, solve for $x$.

Step2: Analyze Option A

$x(x-6)=0$ gives $x=0$ or $x=6$. Two x-intercepts.

Step3: Analyze Option B

$(x-6)(x-6)=0$ gives $x=6$ (double root). x-intercept at $(6,0)$.

Step4: Analyze Option C

$(x+6)(x-6)=0$ gives $x=-6$ or $x=6$. Two x-intercepts.

Step5: Analyze Option D

$(x+6)(x+6)=0$ gives $x=-6$ (double root). Only one x-intercept at $(-6,0)$.

Answer:

D. $f(x) = (x + 6)(x + 6)$