What is the vertex form of #y=x^2+8x+14 #?

1 Answer
Jan 30, 2016

# y = (x + 4)^2 - 2#

Explanation:

the standard form of a parabola is # y = ax^2 + bx + c#

compare to # y = x^2 + 8x + 14 #

to obtain a = 1 , b= 8 and c = 14

The vertex form is : # y =a (x - h )^2 + k #

where (h , k ) are the coordinates of the vertex.

x-coord of vertex #= - b/(2a) = -8/4 = - 2 #

the y-coord = #(-2)^2 + 8(-2) + 14 =8-16+ 14 = -2#

equation is : # y = a(x + 4 )^2 - 2#

in this question(see above ) a = 1

# rArr y = (x+ 4 )^2 - 2 #