Can someone explain this to me, Medal and Fan!!!
Using the completing-the-square method, find the vertex of the function f(x) = 2x2 − 8x + 6 and indicate whether it is a minimum or a maximum and at what point.
Maximum at (2, –2)
Minimum at (2, –2)
Maximum at (2, 6)
Minimum at (2, 6)
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To write in completed square form, the equation has to be in form \[x^2+ax+b\], meaning, it has to be divided by to to have the x^2 with coefficient 1., giving:\[x^2-4x+3\]
Writing in completed square form, consists in putting in brackets squared the x, the sign of a and half its coefficient. At the end, you put the b value with its sign as well, giving\[(x-2)^2-4+3=(x-2)^2-1\]
The equation written is in the form\[(x-p)^2+q\], where x vertex is p and y vertex is q. The coordinates will then be (2,-1).
Look at the sign behind (x-p)^2: It is positive, meaning, the graph is u-shaped. Hence the vertices are at a minimum.