Question #4

Which of the following circles has the greatest number of points of intersection with the parabola x^2 = y + 4?

I thought about this intuitively, thinking that a circle with radius 4 would hit the parabola at its x intercept as well as crossing the parabola at 2 other points, but clearly I was wrong.

Is there a concise mathematical way to solve this?

Question #11

Of the following, which is the best approximation of sqrt(1.5)*(266)^(3/2)?

a) 1,000 b) 2,700 c) 3,200 d) 4,100 e) 5,300

I thought it would simple to use linear approximation on this, setting f(x) = sqrt(x) * 266 ^ (x), but I am having trouble and cannot arrive at a good answer. Is the trick to make 266 a y variable and make the equation f(x,y) = sqrt(x) * (y)^x?

Question #13

A total of x feet of fecing is to form three sides of a level rectangular yard. What is the maximum possible area of the yard, in terms of x?

I thought about it this way:

Area = W x L, from the constraints I know that 2W + L = x or 2L + W = x. Unfortunately, that's about as far as I get.