Math CentralQuandaries & Queries


Question from jessica, a student:

Please help I am banging my head against the wall
Thanks - jess

Use the technique of completing the square to put f(x)= 2x^2-4x+5 in the form f F(x)= a(x-h)^2+k were h,k=vertex of the parabola. identify the coordinate (h,k)of the maximum or minimum point of the associated parabola

Hi Jess,

I'm not sure where you are stuck but I'll see if I can help.

First for completing the square first make sure the coefficient of x2 is 1. So your your function write

f(x) = 2x2 - 4x + 5 = 2(x2 - 2x) + 5

Now look at my answer to a pervious question to complete the square of x2 - 2x, that is find a number a so that x2 - 2x + a is a square. Once you find a you can write

f(x) = 2(x2 - 2x) + 5 = 2(x2 - 2x + a) + 5 - 2a

Try this and see if you can complete the problem.

If you need more assistance write back,

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