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Finding the transformation of a quadratic function $f(x)=ax^2+bx+c$ to $f(nx)$.

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If $f(x)=\\simplify{{n}x^2+{m}x+{c}}$, what is $\\simplify{f({a}x)}$?

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To make the transformation from $f(x)=\\simplify{{n}x^2+{m}x+{c}}$ to $\\simplify{f({a}x)}$, we want to replace the $x$-terms in $f(x)$ with $\\simplify{{a}x}$:

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\\\\[ \\\\begin{split} \\\\simplify{f({a}x)} &\\\\,= \\\\simplify[unitFactor,!expandBrackets,zeroFactor]{{n}({a}x)^2+{m}({a}x)+{c}} \\\\\\\\ &\\\\,= \\\\simplify[unitFactor,!collectNumbers]{{n}({a^2}x^2)+{m*a}x+{c}}. \\\\end{split} \\\\]

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\\\\[ \\\\begin{split} \\\\simplify{f({a}x)} &\\\\,= \\\\simplify[unitFactor,!expandBrackets,zeroFactor]{{n}({a}x)^2+{m}({a}x)+{c}} \\\\\\\\ &\\\\,= \\\\simplify[unitFactor,!collectNumbers]{{n}({a^2}x^2)+{m*a}x+{c}}\\\\\\\\ &\\\\,=\\\\simplify{{n*a^2}x^2+{m*a}x+{c}}. \\\\end{split} \\\\]

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$\\simplify{f(x+{a})}=$[[0]]

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