A and D
A should be pretty obvious. The function shows the profit based upon the price of the tacos. So if the function returns 0, then the profit is 0.
D takes a bit more work. First take the function
y = -4(x-3)^2 + 8
Square the (x-3) term
y = -4(x^2 - 6x + 9) + 8
Distribute the -4 factor
y = -4x^2 + 24x - 36 + 8
Add the -36 and 8 together.
y = -4x^2 + 24x - 28
Now us the quadratic formula with a=-4, b=24, and c=-28 giving you
(-24 - sqrt(128))/(-8) and (-24 + sqrt(128)) / (-8)
Simplify the sqrt(128) to sqrt(64)*sqrt(2) = 8*sqrt(2) giving
(-24 - 8*sqrt(2))/(-8) and (-24 + 8*sqrt(2)) / (-8)
Divide top and bottom by -8 giving
3 + sqrt(2) and 3 - sqrt(2)
Then look at which matches .. C or D? And the answer is D.
