Test 5 Section 4 - #8 (page 652)

This one is based on that all-important fact: parabolas are symmetrical! When they say f(b) = f(3), that's another way of saying that you have two points, (b,y) and (3,y), and the y-values are the same. So look at the graph, and see what that y-value is!

On the graph, I'm seeing the point (3,5), so our other point must be (b,5). The only other place this graph goes through y=5 is at (-1,5), so b must equal -1.

Test 7 Section 3 - #18 (page 773)

This one's a huge pain, and before I get going on it I should stress that it's extremely unlikely that you will see something like this on your SAT...so don't spend too much time worrying about it.  If you want to worry anyway...read on!

Test 3 Section 5 - #18 (page 530)

Ok.  They tell us the equation of that parabola is y = ax².  Whenever you get a question like this (which is not all that uncommon in the hard math questions) you're looking to find a point on the graph!  Since they also tell us that the area of the square is 64, we know the sides of the square must each be 8:

Since parabolas are symmetrical and this one has its minimum at (0,0), we know now what the actual points are at each corner of our square:

And that, friends, is where this gets fun.  Let's use (4,8) since both numbers are positive.  Now that we have a point on our parabola, we just need to plug values in for x and y!

y = ax²

8 = a(4)²

8 = 16a

0.5 = a

This would, of course, also work with (-4,8). Either way, you're going to get 0.5 (or 1/2) for a.