Answer:
(2,1)
Step-by-step explanation:
f(x) = - x^2 + 4x - 3
Factor out the negative
f(x) = - (x^2 - 4x + 3)
Factor
f(x) = -(x-3) (x-1)
The zeros are at
0 = -(x-3) (x-1)
x-3 =0 x-1 =0
x=3 x=1
We know the vertex is 1/2 way between the zeros
(3+1)/2 = 4/2 =2
The x coordinate of the vertex is 2
Substitute x=2 into the equation
f(2) = -(2^2-4(2) +3)
= -(4-8+3)
= -(-1)
= 1
The vertex is (2,1)
