Find turing point from the x intercept form

Question

y=20/7(x-0)(x-13)

Answer 1

To find the turing point from the given equation in x-intercept form y=a(x-p)(x-q), we need to first determine the values of p and q, which are the x-intercepts.

Here, the x-intercepts are 0 and 13.

The turing point is at the vertex of the parabola, which lies on the line of symmetry (x = (p+q)/2 ). Thus, we can calculate the turing point by finding the average of the two x-intercepts:

turing point = ((0+13)/2, f((0+13)/2))

Now, we just need to evaluate the function at the turing point x-coordinate to find the y-coordinate:

turing point = (6.5, f(6.5))

f(x) = 20/7(x-0)(x-13)

f(6.5) = 20/7(6.5-0)(6.5-13)

f(6.5) = 20/7(6.5)(-6.5)

f(6.5) = -380/7

Therefore, the turing point is (6.5, -380/7).