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How do you write #y = (x-2)^2 - 16# in standard form?

Answer 1

Savannah Anderson

#x^2-4x-12#

The standard form of a #color(blue)"quadratic function"# is

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=ax^2+bx+c)color(white)(2/2)|)))#

To obtain #y=(x-2)^2-16" in this form"# expand the brackets and simplify.

#y=(x-2)^2-16=(color(red)(x-2))(x-2)-16#

#=color(red)(x)(x-2)color(red)(-2)(x-2)-16#

#=x^2-2x-2x+4-16#

collecting like terms.

#rArry=x^2-4x-12larr" in standard form"#

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Answer 2

Ethan Adkins

To write the equation y = (x-2)^2 - 16 in standard form, you expand the expression (x-2)^2 and then simplify.

First, expand (x-2)^2: (x-2)^2 = (x-2)(x-2) = x^2 - 4x + 4

Now, substitute this expansion into the original equation: y = x^2 - 4x + 4 - 16 y = x^2 - 4x - 12

To complete the standard form, rearrange the terms so that the quadratic term (x^2) comes first, followed by the linear term (x), and then the constant term: y = x^2 - 4x - 12

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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.