Mrs.Robertson sells online math and reading games. His revenue for each game (in dollars) is modeled by the given equations, where x is the number of days since the games went on sale.
Math Game: M(d)=2x^2+8x+2
Reading Game: R(d)=3x+5
Solve the system algebraically. After how many days is the revenue for each game the same? Show your work and explain your answer.
Graph this system to show the solutions. Label each axis appropriately.

The reading game equation is 3x + 5. That means that every day the game is for sale he will make $3. The math game is parabolic and doesn't have a slope for which to make the same statement about the amount of money made per day. Where they intersect is where the revenue for each will be the same. On the x axis we have the number of days and on the y axis we have the number of dollars. Solving them algebraically:

[tex]2x^2+8x+2=3x+5[/tex] and get everything on one side and set it equal to 0:

[tex]2x^2+5x-3=0[/tex] and factor that however you have learned to factor that quadratic to get:

x = 1/2, -3

The x value indicates the number of days that it would take for the revenue for the games to be the same. Since time can never be negative, we discount the value of -3 and say that it would take 1/2 of a day for the revenue for the games to be the same. As far as the graph goes, I attached a pic below. The red line is the reading game graph and the blue line is the math game parabola. We only need the first quadrant when we graph something like this because, again, days can never be negative so quadrant 2 and 3 are out where x is negative; likewise, the number of dollars will never be negative either, so quadrants 3 and 4 are out. Where those 2 graphs intersect is the number of days that the revenues are the same.