Consider the graph of a quadratic function:

y= 2x^2-3x+1

Translate the (x,y) co-ordinate axes horizontally and vertically, so that the new origin of the co-ordinates system is located at the point with the old co-ordinates (3,5).
The new (X,Y) co-ordinates are therefore related to the old (x,y) system by the equations:
X= x-
Y= y-

Substitute these into the formula y=F(x) above, in order to express Y as a function of X. (Be sure to write the simplest form)
Y=

Thanks so much guys

2. Re: Quadratic Function desperate help!

The entire coordinate axes are shifted up by 5 units, and to the right by 3 units. So where (X,Y) are the new coordinates, we see that when (X,Y)=(0,0), in the language of the old coordinates, (x,y)=(3,5).

So we see that the relationship between the new and old coordinates are X = x - 3 and Y = y - 5. You can verify this yourself: substituting X=0 and Y=0 will force x=3 and y=5.

Now we rearrange the relationship between the new and old coordinate axes so that the old axes are the subject, that is, x = X + 3 and y = Y + 5. Now substitute x and y into the quadratic function to receive the parabola in the language of the new coordinate axes.

Hope this helps.

3. Re: Quadratic Function desperate help!

Thank you so much!

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