   SEARCH HOME Math Central Quandaries & 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,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.