Which of the following are irrational numbers? a. pie (the number lol) b. 4.8 repeating c. square root of 9 d. all of the above

is the only irrational number on the list. As a reminder, an irrational number is one which can't be written as a ratio of two integers.

With a little scratch work, we can show that can be written this way:

And , which can be written as a ratio like , or any other where the numerator is 3 times larger than the denominator.

A proof of the irrationality of is pretty involved and advanced, so you'll just have to take my word for it for now!

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

answer: are you

step-by-step explanation: