The break even point is where profit is zero so set the equation equal to zero and solve

-2x^2+16x-30=0. [divide both sides by -2]

x^2 -8x +15=0 [factor]

(x-3)(x-5)=0 so x=3 and x=5 are the solutions. Since these represent hundreds of thousands answer is

300,000 and 500,000 games

The maximum profit is maximum value of p which would be at the vertex since this is a downward facing parabola. So all we need to do to answer the next part is to find the vertex. the x value will represent the number of games and the y value will be the profit

The x coordinate of the vertex is at -b/2a= -16/-4= 4

f(4) = -2(4^2) +16(4) -30=. -32 + 64 -30=2

So Max profit = $2,000,000 producing 400,000 games

Stephen K.

14d

Ana L.

Thank you!!! If its not too much trouble, I have been stuck on this question for a while: "Two parables are defined by y = 14x - x^2 and y = 2x^2 - 20x. What is the distance between their maximum and minimum values?" I know I have to rearrange the function and find out if I have to find the min/max value, but I'm lost from there. Sorry if I'm being annoying14d

Stephen K.

14d

Ana L.

THANK YOU SO MUCH YOU DONT UNDERSTAND HOW MUCH I NEEDED THIS SERIOUSLY!! (: YOURE INCREDIBLE14d

Ana L.

thank you!! i thought i was gonna fail this assignment but u came through thank youuuuu(:14d