Answer:
f(x) = -(x - 2)^2 + 1
or in standard form it is
f(x) = -x^2 + 4x - 3.
Explanation:
The graph opens downwards so the leading coefficient is negative. The vertex is at x = 2 and y = 1 so we can write the equation in vertex form as:
f(x) = a(x - 2) + 1 where a is some constant.
Now the zeroes of the function are (1, 0 ) and (3, 0).
So we can plug in one of these ( say (1,0) ) into the equation to find the value of a:
0 = a(1 - 2) + 1
0 = a - 2a + 1
0 = -a + 1
a = 1
So our equation is -1(x - 2)^2 + 1
= -( x - 2)^2 + 1