SOLUTION: What is the equation y=x^-14x+50 in vertex form and what is the vertex?

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Question 172409: What is the equation y=x^-14x+50 in vertex form and what is the vertex?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-14x%2B50 Start with the right side of the equation.


Take half of the x coefficient -14 to get -7. In other words, %281%2F2%29%28-14%29=-7.


Now square -7 to get 49. In other words, %28-7%29%5E2=%28-7%29%28-7%29=49


x%5E2-14x%2Bhighlight%2849-49%29%2B50 Now add and subtract 49. Make sure to place this after the "x" term. Notice how 49-49=0. So the expression is not changed.


%28x%5E2-14x%2B49%29-49%2B50 Group the first three terms.


%28x-7%29%5E2-49%2B50 Factor x%5E2-14x%2B49 to get %28x-7%29%5E2.


%28x-7%29%5E2%2B1 Combine like terms.


So after completing the square, x%5E2-14x%2B50 transforms to %28x-7%29%5E2%2B1. So x%5E2-14x%2B50=%28x-7%29%5E2%2B1.


So y=x%5E2-14x%2B50 is equivalent to y=%28x-7%29%5E2%2B1.


So the equation y=%28x-7%29%5E2%2B1 is now in vertex form y=a%28x-h%29%5E2%2Bk where a=1, h=7, and k=1


Remember, the vertex of y=a%28x-h%29%5E2%2Bk is (h,k).


So the vertex of y=%28x-7%29%5E2%2B1 is (7,1).