Question

multiple-choice question using symmetry, what must the y-coordinate be when x = 6? (6,6) (6,4) (6,1) (6,0)

Explanation:

Step1: Find parabola vertex axis

The function is $f(x)=x^2-8x+16$, which factors to $f(x)=(x-4)^2$. This is a parabola with vertex at $x=4$, so its axis of symmetry is $x=4$.

Step2: Find symmetric x-value

For $x=6$, its symmetric point across $x=4$ is calculated as:
$4 - (6 - 4) = 2$
So the symmetric x-value is $x=2$.

Step3: Match y-values via symmetry

From the table, when $x=2$, $f(2)=1$. By symmetry, $f(6)=f(2)$.

Answer:

C. (6,1)