How do you write the quadratic in vertex form given #y= -2x^2-4x-7#?

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Answer 1 · 2015-04-29T08:40:18

The vertex form of a quadratic function is given by
#y = a(x - h)^2 + k#, where #(h, k)# is the vertex of the parabola.

We can use the process of Completing the Square to get this into the Vertex Form.

#y=-2x^2-4x-7#

#-> y + 7 = -2x^2 - 4x# (Transposed -7 to the Left Hand Side)

#-> y + 7 = -2(x^2 + 2x)# (Made the coefficient of #x^2# as 1)

Now we subtract #2# from each side to complete the square

#-> y + 7 - 2 = -2(x^2 + 2x + 1^2)#

#-> y + 5 = -2(x+1)^2 #

#-> y + 5 = -2{x-(-1)}^2 #

# -> color(green)(y = -2{x - (-1)}^2 + (-5)# is the Vertex Form

The vertex of the Parabola is# {-1 , -5}#