How do I write a quadratic function whose zeroes are 2 and 6?

Answer 1

f(x) = (x-2)(x-6)

In standard form, this would be f(x) = x² -8x +12

NOTE that there are an infinite number of quadratic functions that have zeros at 2 and 6.

They are all given by f(x) = a(x-2)(x-6), where a is any real number other than zero.

Answer 2

If 2 is a zero, then (x - 2) is a factor. And if 6 is a zero, then (x - 6) is also a factor. So the quadratic could be:

y = (x - 2)(x - 6)

You could multiply this out to get:

y = x² - 8x + 12