SOLUTION: find the equation of the normal to the curve y=3+2x-x^2 which is parallel to the line 2y-x=3

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Question 1149607: find the equation of the normal to the curve y=3+2x-x^2 which is parallel to the line 2y-x=3
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The derivative of the function for the given curve is the slope of the curve at any point.

y+=+3%2B2x-2x%5E2
dy%2Fdx+=+2-2x

The slope of the given line is 1/2; we want the slope of the normal to the curve to also be 1/2. That means we want the slope of the curve at that point to be -2.

2-2x+=+-2
4+=+2x
x+=+2

y+=+f%28x%29+=+3%2B2%282%29-2%5E2+=+3

The slope is 1/2; the point on the curve is (2,3). The equation of the normal is

y+=+%281%2F2%29x%2B2

A graph, showing the given curve (red), the given line (green), and the normal to the curve parallel to the given line (blue).

graph%28400%2C400%2C-2%2C4%2C-1%2C5%2C3%2B2x-x%5E2%2C.5x%2B1.5%2C.5x%2B2%29