Question

Complete the square to write f(x) = x2 + 6x + 14 in vertex form. a. f(x) = (x + 3)2 + 5 b. f(x) = (x - 3)2 + 14 C. f(x) = (x + 3)2 + 23 d. f(x) = (x + 6)2 + 14

Answer 1

f(x) = x^2 + 6x + 14

Equation is written in ax^2 + bx + c form

where:

a= 1

b= 6

c=14

Consider the vertex:

a (x+d) ^2 + e

d= b/2a = 6 / 2 (1) = 3

e = c- b^2/4a = 14 - [6^2/4(1) ] = 5

Substitute d and e in the vertex form:

f(x)= 1 (x + 3 ) ^2 + 5

f(x) = (x+3)^2 + 5

option a