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

Answer:

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

Explanation:

Step1: Recall x - intercept formula

Set $f(x)=0$.

Step2: Analyze option A

For $f(x)=x(x - 6)$, set $f(x)=0$, then $x(x - 6)=0$. By zero - product property, $x = 0$ or $x=6$. So it has two x - intercepts.

Step3: Analyze option B

For $f(x)=(x - 6)(x - 6)=(x - 6)^2$, set $f(x)=0$, then $(x - 6)^2=0$, and $x = 6$. It has one x - intercept at $(6,0)$.

Step4: Analyze option C

For $f(x)=(x + 6)(x - 6)$, set $f(x)=0$. By zero - product property, $x+6 = 0$ or $x - 6=0$, so $x=-6$ or $x = 6$. It has two x - intercepts.

Step5: Analyze option D

For $f(x)=(x + 6)(x + 6)=(x + 6)^2$, set $f(x)=0$. Then $(x + 6)^2=0$. Solving for $x$, we get $x=-6$. It has only one x - intercept at $(-6,0)$.