Hi Mike, Can you please explain Question 11, Test 6, section 3 ? I know the parabola opens downward, but I’m confused after that. Thanks.

You’ve already got the first part—when you add a negative to the front of a parabola you’ll flip it vertically. Since this parabola begins facing up, the negative flips it so it faces down.

From there, I think it’s helpful to think about this in terms of how functions shift. For some function *f*(*x*) that’s graphed on the *xy*-plane:

*f*(*x*)+1 ⇒ (graph moves UP one)*f*(*x*)–1 ⇒ (graph moves DOWN one)*f*(*x*+1) ⇒ (graph moves LEFT one)*f*(*x–*1) ⇒ (graph moves RIGHT one)

That applies here. You’re basically taking the function and applying a few shifts (and a flip). Check it out–if you start by assuming a function , you can build the function in this question by shifting that original function:

flips the function upside-down, then shifts it *b* units to the right and *c* units up.

If you hate everything I’ve just said, I have good news! You can also just memorize the vertex form of a parabola (which we basically just derived).

If you have a parabola in the form , then you know it has its vertex at and that the sign of *a* tells you whether the parabola opens up or down. This question basically gives you the vertex form, only it uses *b* and *c* instead of *h* and *k*. Recognize that and you know right away that the parabola’s vertex is at .