Question

A quadratic function, f(x), has one zero at (0, 0) and a maximum value at (1, 1). Is it possible to find the second zero of f(x)? If it is possible, then is it also possible find f(x)? Justify your answer.

Answer 1

It is possible to find the zero and f(x).

Other zero is (2, 0).

f(x) = -x(x - 2).

Explanation:

As one of the zeroes is at (0,0) the function will be of the form:

y = -ax(x - b) where b = the other zero and a is a constant.

The negative coefficient is there because the quadratic has a maximum value as it opens downwards.

As the curve is symmetric about x = 1 ( because the vertex is at 1,1) the second zero is at (2, 0). So b = 2.

As the vertex is at (1, 1) the value of a is also 1.