The quadratic function f with zeros at 2 and -12 can be written in factored form as follows:
f(x) = a(x - 2)(x + 12)
To find the value of "a" in the equation, we can use a point on the graph of the quadratic function. Let's say we know that f(0) = 36.
Substituting x = 0 and f(x) = 36 into the equation, we get:
36 = a(0 - 2)(0 + 12)
36 = a(-2)(12)
36 = a(-24)
a = -36/24
a = -3/2
Now we can write the quadratic function f(x) with the given zeros:
f(x) = (-3/2)(x - 2)(x + 12)
This function will have zeros at x = 2 and x =-12.