josh has to graph a set of parabolas of the form y=x^2 -4x+2^n where n is an integer and 0≤n≤6 what is the probability that one of these parabolas, chosen at random, will have :
a)one x intercept
b)two x intercepts
c)no x intercept
look at the discriminant. It determines the number of real roots that exist.
In this case, the discriminant is 16-4*2^n = 4(4-2^n)
So, now it becomes easy.
a) 4-2^n = 0
b) 4-2^n > 0
c) 4-2^n < 0
hit: 4 = 2^2