# The graph of y=x^2+3x is shifted 3 units to the right. This graph is then vertically stretched by a factor of 6 and reflected across the x-axis. Finally, the graph is shifted 8 units upwardWRITE THE EQUATION

1
by sweetysiri92

2014-10-16T09:15:30+05:30

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y = x² + 3 x

New axes are X and Y.

Shift right,            X = x + 3

Stretch vertically by a factor of 6 :  Y = 6y

Reflected across x-axis :      Y becomes  -Y       =>    Y = -6y

Graph shifted 8 units upwards :  Y becomes Y+8    =>  Y = -6y+8

So,  x = X-3  and  y = (8-Y)/6

Substitute this in the original equation for the graph:

(8-Y)/6 = (X-3)² + 3 (X-3) = (X-3)(X-3+3) = X² - 3X

8 - Y = 6 X² - 18 X
Y = 8 - 6 X² + 18 X             or     Y = -6 (X - 3/2)² + 43/2

So  equation of the graph:  y = 8 - 6 x² + 18 x    or  -6 (x - 3/2)² + 43/2

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