A quadratic function f (x) attains its minimum value of –15 at x = 3. If f (0) = 5, find the value of f (9).

The given quadratic function f(x) attains its minimum value at x = 3. This means that the vertex of the parabola is at (3, -15).

A quadratic function is generally given by f(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola.

So, the given function can be written as f(x) = a(x-3)² - 15.

We also know that f(0) = 5. Substituting these values in the equation we get:

5 = a(0-3)² - 15 5 = 9a - 15 9a = 20 a = 20/9

So, the function is f(x) = (20/9)(x-3)² - 15.

Now, we need to find the value of f(9). Substituting x = 9 in the equation we get:

f(9) = (20/9)(9-3)² - 15 f(9) = (20/9)(6)² - 15 f(9) = (20/9)*36 - 15 f(9) = 80 - 15 f(9) = 65.