Quadratics question?

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Quadratics question?

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Answer 1 · 2018-04-23T16:59:14

From the unchanging zeros and the halving of the height, it appears $g (x) = \frac{1}{2} f (x)$ $g(x) = 1/2 f(x)$ , choice b.

Explanation:

When we scale the argument, like in $f (2 x)$ $f(2x)$ or $f (\frac{x}{2})$ $f(x/2)$ , that stretches or compresses in the $x$ $x$ direction, which isn't happening here.

When we scale like $\frac{1}{2} f (x)$ $1/2 f(x)$ or $2 f (x)$ $2 f(x)$ that compresses or stretches in the $y$ $y$ direction. That seems like what's going on.

The function is unchanged when $f (x) = 0$ $f(x)=0$ (around $x = - 8$ $x=-8$ and $x = 0$ $x=0$ ) which is consistent with $y$ $y$ scaling.

The height at the apex at $x = 4$ $x=4$ went from $3$ $3$ to $\frac{3}{2}$ $3/2$ indicative of a $y$ $y$ scale factor of $\frac{1}{2}$ $1/2$ . That looks right in general.

So it appears $g (x) = \frac{1}{2} f (x)$ $g(x) = 1/2 f(x)$ , choice b.

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