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ASHA 777 [7]
3 years ago
9

Which equation is y = 3(x – 2)2 – (x – 5)2 rewritten in vertex form?

Mathematics
1 answer:
Alenkinab [10]3 years ago
4 0
Y= 3( x -2 )² - ( x-5 )² = 3 ( x² - 4 x + 4 ) - ( x² - 10 x + 25 ) =
= 3 x² - 12 x + 12 - x² + 10 x - 25=
= 2 x² - 2 x - 13 =
= 2 ( x² - x + 1/4 - 1/4 ) - 13 =
= 2 ( x - 1/2 )² - 1/2 - 26/2 =  2 ( x - 1/2 )² - 27/2
Answer: D) 
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3 years ago
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jarptica [38.1K]
First we'll do two basic steps. Step 1 is to subtract 18 from both sides. After that, divide both sides by 2 to get x^2 all by itself. Let's do those two steps now

2x^2+18 = 10
2x^2+18-18 = 10-18 <<--- step 1
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At this point, it should be fairly clear there are no solutions. How can we tell? By remembering that x^2 is never negative as long as x is real. 

Using the rule that negative times negative is a positive value, it is impossible to square a real numbered value and get a negative result. 

For example
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So x^2 = -4 has no real solutions. Taking the square root of both sides leads to

x^2 = -4
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