SOLUTION: write the quadratic function in vertex form: y=2x^2+11x+8

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Question 549192: write the quadratic function in vertex form:
y=2x^2+11x+8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2%2B11x%2B8 Start with the given expression.


2%28x%5E2%2B%2811%2F2%29x%2B4%29 Factor out the x%5E2 coefficient 2. 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%2811%2F2%29=11%2F4.


Now square 11%2F4 to get 121%2F16. In other words, %2811%2F4%29%5E2=%2811%2F4%29%2811%2F4%29=121%2F16


2%28x%5E2%2B%2811%2F2%29x%2Bhighlight%28121%2F16-121%2F16%29%2B4%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.


2%28%28x%5E2%2B%2811%2F2%29x%2B121%2F16%29-121%2F16%2B4%29 Group the first three terms.


2%28%28x%2B11%2F4%29%5E2-121%2F16%2B4%29 Factor x%5E2%2B%2811%2F2%29x%2B121%2F16 to get %28x%2B11%2F4%29%5E2.


2%28%28x%2B11%2F4%29%5E2-57%2F16%29 Combine like terms.


2%28x%2B11%2F4%29%5E2%2B2%28-57%2F16%29 Distribute.


2%28x%2B11%2F4%29%5E2-57%2F8 Multiply.


So after completing the square, 2x%5E2%2B11x%2B8 transforms to 2%28x%2B11%2F4%29%5E2-57%2F8. So 2x%5E2%2B11x%2B8=2%28x%2B11%2F4%29%5E2-57%2F8.


So y=2x%5E2%2B11x%2B8 is equivalent to y=2%28x%2B11%2F4%29%5E2-57%2F8 which is the answer in vertex form.