Question

Which point gives the vertex of f(x) = - x2 + 4x - 3?

A) (2,-1)
B) (-2,-13)
C) (2,1)
D) (2,-13)

Answer 1

(2,1)

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)