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?

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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?

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Answer 1 · 2017-11-19T14:45:32

$y = \frac{12}{245} x^{2} + \frac{4}{35} x$ $y=12/245x^2+4/35x$

Explanation:

Let $f (x) = 3 x^{2} + 2 x$ $f(x)=3x^2+2x$

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

This gives us $f (\frac{2}{7} x)$ $f(2/7x)$
Combining these, we get $5 f (\frac{2}{7} x)$ $5f(2/7x)$

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

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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?

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