Question

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?

Answer 1

`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`