After transforming f(x) = 2x2 + 4x + 3 into vertex form, the vertex is easily identifiable. Which ordered pair is the vertex?

Question

A. (0, 3)

B. (1, 1)

C. (-1, 1)

D. (-3, 0)

Answer 1

y=2x²+4x+3

y=2(x²+2x+3/2)

y=2(x²+2x+1 +1/2)   Using the formula for completing the square (x+a)²=x²+2ax+a².  In our example a=1.

y=2(x²+2x +1) +1

y-1=2(x+1)²

So the vertex is (-1,1)

Answer 2

f(x) in vertex form is

 

f(x) = a(x - h)² + k

 

 

where   vertex is (h, k).

 

 

f(x) = 2(x² + 2x + 1) + 1

 

f(x) = 2(x + 1)(x + 1) + 1

 

f(x) = 2(x + 1)² + 1

 

 

h = -1

k = 1