What is the standard form of $y = {(x - 3)}^{2} + 3$ $y=(x-3)^2+3$ ?

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What is the standard form of $y = {(x - 3)}^{2} + 3$ $y=(x-3)^2+3$ ?

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Answer 1 · 2016-03-18T21:22:25

$y = x^{2} - 6 x + 12$ $y = x^2 -6x + 12$

Explanation:

Multiply out the brackets and collect like terms.

${(x - 3)}^{2} = (x - 3) (x - 3) = x^{2} - 3 x - 3 x + 9$ $(x - 3)^2 = (x - 3 )(x - 3 ) = x^2 - 3x - 3x + 9$

$\Rightarrow y = x^{2} - 6 x + 9 + 3 = x^{2} - 6 x + 12$ $rArr y = x^2 - 6x + 9 + 3 = x^2 - 6x + 12$

Writing an answer in standard form means , start with the term that has the highest power of the variable , in this case $x^{2}$ $x^2$
Followed by terms with decreasing powers until the last term , usually a constant.

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What is the standard form of $y = {(x - 3)}^{2} + 3$ $y=(x-3)^2+3$ ?

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