Question

which function has only one x-intercept at $(-6, 0)$?$\bigcirc$ $f(x) = x(x - 6)LXB0\bigcirc$ $f(x) = (x + 6)(x - 6)$$\bigcirc$ $f(x) = (x + 6)(x + 6)$

Explanation:

Step1: Find roots of option 1

Set $f(x)=0$: $x(x-6)=0$
Roots: $x=0, x=6$

Step2: Find roots of option 2

Set $f(x)=0$: $(x-6)(x-6)=0$
Roots: $x=6$ (double root)

Step3: Find roots of option 3

Set $f(x)=0$: $(x+6)(x-6)=0$
Roots: $x=-6, x=6$

Step4: Find roots of option 4

Set $f(x)=0$: $(x+6)(x+6)=0$
Roots: $x=-6$ (double root)

Answer:

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