What is the equation of the quadratic function with a vertex at (2,-25), and an x-intercept at (7,0)

f (x) = x^2 - 4x - 21.

Step-by-step explanation:

Since the vertex is at (2, - 25) we can write the vertex form as:

y = f (x) = a (x - 2) ^2 - 25

Given the x-intercept (7, 0), x = 7 when y = 0, so substituting:

0 = a (7 - 2) ^2 - 25

0 = 25a - 25

giving a = 1.

So our equation is f (x) = (x - 2) ^2 - 25.

Converting to standard form

f (x) = x^2 - 4x + 4 - 25

f (x) = x^2 - 4x - 21.