How do you write #Y=-6(x-2)^2-9# in standard form?

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Answer 1 · 2017-10-06T00:19:49

#y=-6x^2+24x-33#

Standard form for a quadratic is #y=ax^2+bx+c#

The best way to do this is to simplify using order of operations.

First exponents,

#(x-2)^2=(x-2)(x-2)#
Using FOIL #x*x=x^2, x*-2=-2x, -2*x=-2x, and -2*-2=4#

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

Next multiplication,

#-6(x^2-4x+4)=-6x^2+24x-24#

Finally subtraction,

#-6x^2+24x-24-9=-6x^2+24x-33#