Question

which function has two x-intercepts, one at (0, 0) and one at (4, 0)?
$f(x) = x(x - 4)$
$f(x) = x(x + 4)$
$f(x) = (x - 4)(x - 4)$
$f(x) = (x + 4)(x + 4)$

Explanation:

Step1: Recall x-intercept rule

To find x-intercepts, set $f(x)=0$ and solve for $x$.

Step2: Test Option 1: $f(x)=x(x-4)$

Set $x(x-4)=0$. By zero product property, $x=0$ or $x-4=0 \implies x=4$. Intercepts: $(0,0)$ and $(4,0)$.

Step3: Test Option 2: $f(x)=x(x+4)$

Set $x(x+4)=0$. Solutions: $x=0$ or $x=-4$. Intercepts: $(0,0)$ and $(-4,0)$.

Step4: Test Option 3: $f(x)=(x-4)(x-4)$

Set $(x-4)^2=0$. Solution: $x=4$ (double root). Intercept: $(4,0)$.

Step5: Test Option 4: $f(x)=(x+4)(x+4)$

Set $(x+4)^2=0$. Solution: $x=-4$ (double root). Intercept: $(-4,0)$.

Answer:

A. $f(x) = x(x - 4)$