1. The amount of money a certain company makes can be represented by the graph $y=x^2-8x-33$, where $x$ is the quantity produced. What is the smallest quantity at which the company can produce to break even or make a profit?
2. The $y = -6t^2 + 43t$ equation describes the height (in feet) of a projectile $t$ seconds after it is launched from the surface of Mars at 43 feet per second. In how many seconds will the projectile first reach 77 feet in height? Express your answer as a decimal rounded to the nearest tenth.
y = x^2 - 8x - 33
We want to solve this
x^2 - 8x - 33 = 0 factor
(x - 11) ( x + 3) = 0
The first factor set to 0 is what we need
x - 11 = 0
x = 11 = the minimum units needed to break even