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.