SOLUTION: x2(squared)+5x-24 in vertex form?

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Question 302481: x2(squared)+5x-24 in vertex form?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B5x-24 Start with the given expression.


Take half of the x coefficient 5 to get 5%2F2. In other words, %281%2F2%29%285%29=5%2F2.


Now square 5%2F2 to get 25%2F4. In other words, %285%2F2%29%5E2=%285%2F2%29%285%2F2%29=25%2F4


x%5E2%2B5x%2Bhighlight%2825%2F4-25%2F4%29-24 Now add and subtract 25%2F4. Make sure to place this after the "x" term. Notice how 25%2F4-25%2F4=0. So the expression is not changed.


%28x%5E2%2B5x%2B25%2F4%29-25%2F4-24 Group the first three terms.


%28x%2B5%2F2%29%5E2-25%2F4-24 Factor x%5E2%2B5x%2B25%2F4 to get %28x%2B5%2F2%29%5E2.


%28x%2B5%2F2%29%5E2-121%2F4 Combine like terms.


So after completing the square, x%5E2%2B5x-24 transforms to %28x%2B5%2F2%29%5E2-121%2F4. So x%5E2%2B5x-24=%28x%2B5%2F2%29%5E2-121%2F4.


So y=x%5E2%2B5x-24 is equivalent to y=%28x%2B5%2F2%29%5E2-121%2F4.


So the equation y=%28x%2B5%2F2%29%5E2-121%2F4 is now in vertex form y=a%28x-h%29%5E2%2Bk where a=1, h=-5%2F2, and k=-121%2F4


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


So the vertex of y=%28x%2B5%2F2%29%5E2-121%2F4 is (-5/2,-121/4).