Home > Algebra > Vertex Form of a Quadratic Equation

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

Answer 1

Julia Adams

See a solution process below:

We can use this rule to expand the term in parenthesis:

#(color(red)(x) - color(blue)(y))^2 = color(red)(x)^2 - 2color(red)(x)color(blue)(y) + color(blue)(y)^2#

#y = (color(red)(x) - color(blue)(2))^2 + 6#

#y = color(red)(x)^2 - (2 * color(red)(x) * color(blue)(2)) + color(blue)(2)^2 + 6#

#y = x^2 - 4x + 4 + 6#

#y = x^2 - 4x + 10#

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Answer 2

Kennedy Adams

To write the equation (y = (x - 2)^2 + 6) in standard form, expand the squared term and simplify:

(y = (x - 2)^2 + 6)

(y = (x - 2)(x - 2) + 6)

(y = x^2 - 4x + 4 + 6)

(y = x^2 - 4x + 10)

So, the standard form of the equation is (y = x^2 - 4x + 10).

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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.