Determine a quadratic function with this set of characteristics.

Question

x-intercepts of 2 and 7 and maximum value of 25

( How would I find the x-coordinate for the vertex?)

(Thank you!)

Answer 1

given the x-intercepts,

y = a(x-2)(x-7)
The vertex is midway between the roots, at x = 9/2

y(9/2) = a(5/2)(-5/2) = -25/4 a
Since we want y(9/2) = 25, a = -4

y = -4(x-2)(x-7)

See

http://www.wolframalpha.com/input/?i=-4%28x-2%29%28x-7%29

Answer 2

25 is the maximum value

I used x = 9/2 and I got this equation:

-4(x-4.5)^2+25