Question

Which point gives the vertex of ƒ(x) = –x2 + 4x – 3?

Answer 1

Answer:

The vertex is (2,1)

Step-by-step explanation:

ƒ(x) = –x^2 + 4x – 3

Factor out the negative

   = -(x^2 -4x+3)

 Factor

What 2 numbers multiply to +3 and add to -4

-3*-1 = 3

-3+-1 = -4

f(x) =  -( x-3)(x-1)

Find the zeros

0 = -( x-3)(x-1)

0 = x-3   0 = x-1

x=3            x=1

The x value of the vertex is 1/2 way between the two zeros

(3+1)/2 = 4/2 =2

To find the y value, substitute x=2 in

f(2) =  -( 2-3)(2-1)

       =-(-1)(1) = 1

The vertex is (2,1)