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.

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

Other zero is (2, 0).

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

Step-by-step 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.