SOLUTION: Put {{{x=5y^2-25y+60}}} in the form {{{x=a(y-k)^2+h}}}

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Question 152795This question is from textbook Algebra 2 Texas
: Put x=5y%5E2-25y%2B60 in the form x=a%28y-k%29%5E2%2Bh This question is from textbook Algebra 2 Texas

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

5y%5E2-25y%2B60 Start with the given expression.


5%28y%5E2-5y%2B12%29 Factor out the y%5E2 coefficient 5. This step is very important: the y%5E2 coefficient must be equal to 1.


Take half of the y coefficient -5 to get -5%2F2. In other words, %281%2F2%29%28-5%29=-5%2F2.


Now square -5%2F2 to get 25%2F4. In other words, %28-5%2F2%29%5E2=%28-5%2F2%29%28-5%2F2%29=25%2F4


5%28y%5E2-5y%2Bhighlight%2825%2F4-25%2F4%29%2B12%29 Now add and subtract 25%2F4 inside the parenthesis. Make sure to place this after the "y" term. Notice how 25%2F4-25%2F4=0. So the expression is not changed.


5%28%28y%5E2-5y%2B25%2F4%29-25%2F4%2B12%29 Group the first three terms.


5%28%28y-5%2F2%29%5E2-25%2F4%2B12%29 Factor y%5E2-5y%2B25%2F4 to get %28y-5%2F2%29%5E2.


5%28%28y-5%2F2%29%5E2%2B23%2F4%29 Combine like terms.


5%28y-5%2F2%29%5E2%2B5%2823%2F4%29 Distribute.


5%28y-5%2F2%29%5E2%2B115%2F4 Multiply.


So after completing the square, 5y%5E2-25y%2B60 transforms to 5%28y-5%2F2%29%5E2%2B115%2F4. So 5y%5E2-25y%2B60=5%28y-5%2F2%29%5E2%2B115%2F4.


So x=5y%5E2-25y%2B60 is equivalent to x=5%28y-5%2F2%29%5E2%2B115%2F4.


This means that the equation x=5%28y-5%2F2%29%5E2%2B115%2F4 is in the form x=a%28y-k%29%5E2%2Bh where a=5, h=5%2F2, and k=115%2F4