Test 3 Section 3 Number 12?

This is one of my favorite questions! All you’re told is that y=a(x-2)(x+4) has its vertex at (c,d), and then you’re asked for an expression for d, the y-coordinate of the vertex.

The way to get this is to recognize that the factored form you’re given is already giving you the x-coordinate of the vertex. If the parabola can be factored to y=a(x-2)(x+4), then you know it has zeros at x = 2 and x = –4. Because all parabolas are symmetrical, you know that the x-coordinate of the vertex must be right smack between those zeros (i.e., at the average of those zeros). \dfrac{-4+2}{2}=-1, so the x-coordinate of the vertex is –1.

Now all you need to do is plug –1 in for x to find the y-coordinate of the vertex.

    \begin{align*}y&=a(-1-2)(-1+4)\\y&=a(-3)(3)\\y&=-9a\end{align*}

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