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

1 Answer
Jim G.
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

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