If the graph of y=3x^2+2x is vertically stretched by a factor of 9 and horizontally stretched by a factor of 7/2, determine the equation that describes the transformed graph?

1 Answer
Tom M.
Nov 19, 2017

#y=12/245x^2+4/35x#

Explanation:

Let #f(x)=3x^2+2x#

A vertical stretch of f(x), SF #a# would be #af(x)# This gives us the first transformation, #5f(x)#
A horizontal stretch, SF #b# would be #f(1/bx)# (the reciprocal of the scale factor).

This gives us #f(2/7x)#
Combining these, we get #5f(2/7x)#

Replacing this back into #y=f(x)#, we get:
#5y=3(2/7x)^2+2(2/7x)#
#5y=12/49x^2+4/7x#
#y=12/245x^2+4/35x#

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