Rearrange 20t-t² in the form p - (t - q)² where p and q are constants
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# Rearrange 20t-t² in the form p - (t - q)² where p and q are constants

[From: ] [author: ] [Date: 11-05-18] [Hit: ]
First factor out a –1 ...Take half the middle coeficient and sqaure it. (–20/2)² = 10² = 100.–1(t² – 20t+ 100) + ___?......
Thank you, please leave calculations so I can check your method, thank you.

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This is just completing the square. First factor out a –1 ...

–1(t² – 20t + ____) + _____

Take half the middle coeficient and sqaure it. (–20/2)² = 10² = 100. Put it in the first blank:

–1(t² – 20t + 100) + ___?__ Now what do you need in the second blank to balance it?

By adding +100 insiode the parentheses that is multiplied by a –1, you have really subtracted 100, so you need to add 100 to keep the expression equal to its original value...

–1(t² – 20t + 100) + 100 Now recocognize the perfect sqaure ...

–(t – 10)² + 100 or in the form you specified: 100 – (t – 10)²

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p- t^2 +2qt -q^2 = 20t -t^2

so, q =10, q^2 =100, hence p =100 ...so,

100 -(t-10)^2
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