SOLUTION: how do you change y=-16x^2+88x+3 to vertex form?

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Question 241771: how do you change y=-16x^2+88x+3 to vertex form?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-16x%5E2%2B88x%2B3 Start with the given right side of the equation.


-16%28x%5E2-%2811%2F2%29x-3%2F16%29 Factor out the x%5E2 coefficient -16. This step is very important: the x%5E2 coefficient must be equal to 1.


Take half of the x coefficient -11%2F2 to get -11%2F4. In other words, %281%2F2%29%28-11%2F2%29=-11%2F4.


Now square -11%2F4 to get 121%2F16. In other words, %28-11%2F4%29%5E2=%28-11%2F4%29%28-11%2F4%29=121%2F16


-16%28x%5E2-%2811%2F2%29x%2Bhighlight%28121%2F16-121%2F16%29-3%2F16%29 Now add and subtract 121%2F16 inside the parenthesis. Make sure to place this after the "x" term. Notice how 121%2F16-121%2F16=0. So the expression is not changed.


-16%28%28x%5E2-%2811%2F2%29x%2B121%2F16%29-121%2F16-3%2F16%29 Group the first three terms.


-16%28%28x-11%2F4%29%5E2-121%2F16-3%2F16%29 Factor x%5E2-%2811%2F2%29x%2B121%2F16 to get %28x-11%2F4%29%5E2.


-16%28%28x-11%2F4%29%5E2-31%2F4%29 Combine like terms.


-16%28x-11%2F4%29%5E2-16%28-31%2F4%29 Distribute.


-16%28x-11%2F4%29%5E2%2B124 Multiply.


So after completing the square, -16x%5E2%2B88x%2B3 transforms to -16%28x-11%2F4%29%5E2%2B124. So -16x%5E2%2B88x%2B3=-16%28x-11%2F4%29%5E2%2B124.


So y=-16x%5E2%2B88x%2B3 is equivalent to y=-16%28x-11%2F4%29%5E2%2B124.


So the equation y=-16%28x-11%2F4%29%5E2%2B124 is now in vertex form y=a%28x-h%29%5E2%2Bk where a=-16, h=11%2F4, and k=124


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


So the vertex of y=-16%28x-11%2F4%29%5E2%2B124 is .