What is the vertex form of #y=2x^2 + 2x + 12#?

1 Answer
Jim G.
Feb 23, 2016

# y = 2(x + 1/2 )^2 +23/2 #

Explanation:

The standard form of a quadratic function is #y = ax^2 + bx + c#

The function # y = 2x^2 + 2x + 12 " is in this form "#

and by comparison , a = 2 , b = 2 and c = 12

The vertex form of the equation is #y = a(x - h )^2 + k#
where (h , k ) are the coordinates of the vertex.

x-coord of vertex (h ) #= (-b)/(2a) = (-2)/4 = -1/2 #

and y-coord (k) =#2(-1/2)^2 + 2(-1/2) + 12 = 1/2 - 1 + 12 = 23/2#

here #(h , k ) = (-1/2 , 23/2 ) and a = 2#

#rArr y = 2(x + 1/2 )^2 + 23/2 " is equation in vertex form "#

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