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

Answer 1

Hazel Anglin

#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#

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Answer 2

Kennedy Adams

To write the equation ( Y = -6(x - 2)^2 - 9 ) in standard form, you can expand and simplify the expression:

[ Y = -6(x^2 - 4x + 4) - 9 ] [ Y = -6x^2 + 24x - 24 - 9 ] [ Y = -6x^2 + 24x - 33 ]

So, the equation in standard form is: ( Y = -6x^2 + 24x - 33 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.