SOLUTION: What are the coordinates of the turning point for the graph of the parabola whose equation is y=2x^2+4x-7?

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Question 292650: What are the coordinates of the turning point for the graph of the parabola whose equation is y=2x^2+4x-7?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We essentially want to convert the equation into vertex form. To do that, we need to complete the square. Note: the vertex of the parabola is the turning point.



2x%5E2%2B4x-7 Start with the given expression.


2%28x%5E2%2B2x-7%2F2%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 2 to get 1. In other words, %281%2F2%29%282%29=1.


Now square 1 to get 1. In other words, %281%29%5E2=%281%29%281%29=1


2%28x%5E2%2B2x%2Bhighlight%281-1%29-7%2F2%29 Now add and subtract 1 inside the parenthesis. Make sure to place this after the "x" term. Notice how 1-1=0. So the expression is not changed.


2%28%28x%5E2%2B2x%2B1%29-1-7%2F2%29 Group the first three terms.


2%28%28x%2B1%29%5E2-1-7%2F2%29 Factor x%5E2%2B2x%2B1 to get %28x%2B1%29%5E2.


2%28%28x%2B1%29%5E2-9%2F2%29 Combine like terms.


2%28x%2B1%29%5E2%2B2%28-9%2F2%29 Distribute.


2%28x%2B1%29%5E2-9 Multiply.


So after completing the square, 2x%5E2%2B4x-7 transforms to 2%28x%2B1%29%5E2-9. So 2x%5E2%2B4x-7=2%28x%2B1%29%5E2-9.


So 2x%5E2%2B4x-7=0 is equivalent to 2%28x%2B1%29%5E2-9=0.


So y=2x%5E2%2B4x-7 is equivalent to y=2%28x%2B1%29%5E2-9.


So the equation y=2%28x%2B1%29%5E2-9 is now in vertex form y=a%28x-h%29%5E2%2Bk where a=2, h=-1, and k=-9


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


So the vertex of y=2%28x%2B1%29%5E2-9 is (-1,-9).


This consequently means that the vertex of y=2x%5E2%2B4x-7 is (-1,-9) (since the two equations are equivalent)


So the turning point of y=2x%5E2%2B4x-7 is (-1,-9)