Question

A quadratic function f(x) has one zero at (0,0) and a maximum value at (1,1)
is it possible to determine the second zero
is it possible to determine the equation for f(x)
if it is then determine the zero and/or equation

Answer 1

yes, yes

y = a(x-1)^2 + 1
but (0,0) must satisfy this, so
0 = a(-1)^2 + 1
a = -1

y = -(x-1)^2 + 1
or
y = -x^2 + 2x
for zeros,
-x(x - 2) = 0
x = 0 <---- we knew that one
or
x = 2