At how many points does the graph of y = (x-6)^2 intersect the x-axis?

A: Two.

If x = 6, bang

if x = 6 bang
so at ONE point
x = 6 which is the vertex of the parabola. It just grazes the x axis and both roots are right there.

I'm sorry but I'm slightly confused. How does x = 6 when the graph is y =(x-6)^2?

When x = 6

(x-6) = 0
so
y = 0 when x = 6
That is when it hits the x axis

To determine how many times the graph of y = (x-6)^2 intersects the x-axis, we need to find the number of x-values that make the y-coordinate equal to zero.

For the equation y = (x-6)^2, we can set y to zero and solve for x:

0 = (x-6)^2

Taking the square root of both sides, we get:

√0 = x - 6

0 = x - 6

Adding 6 to both sides:

x = 6

So, we have one value of x, which is 6, that makes the y-coordinate equal to zero. Therefore, the graph of y = (x-6)^2 intersects the x-axis at one point, not two.

Hence, the answer is one, not two.