Suppose that the function f(x) = 2x + 12 represents the cost to rent x movies a month from an internet movie club. makayla now has $10. how many more dollars does makayla need to rent 7 movies next month?

1) This equation is a polynomial to the second power, so lets use the quadratic formula. 

[ -B +- squareroot(B^2 - 4AC) ] / 2A -A bit hard to read without the actual format. 

= [ -20 +- squareroot( 20^2 - (4)(-5)(60) ) ] / (2)(-5) -A corresponds to -5, B to 20, and C to 60. Plug in. 

= [ -20 +- squareroot(400 - (-1200) ) ] / (-10) - Simplifying 

= [-20 +- 40] / (-10) 

Because there is a plus/minus we now have two equations. 

= [-20 - 40] / (-10) and = [-20 + 40] / (-10) 

= 6 = -2 

Now in case you aren't extremely familiar with the quadratic equation, by plugging in each piece and solving, we get the two x-intercepts that this parabola equation crosses and a graph. Lucky for us, this means that the two numbers we solved for is equal to the time at which this object touches the ground. 

Common sense solves the rest. You cant have negative time so -2 is off our list. 

That means it will take 6 seconds for this object to hit the ground.  

2) We have f(x)=2x+12 and x is the amount of movies, and this function gives us the cost of the rental. 

She requires 7 movies, so all we have to do is simply plug in 7 for x. 

f(x) = 2x + 12 

= 2(7) + 12 

= 14 + 12 

= $26 -So the cost for 7 movies will be $26. 

We know she already has $10 so we just subtract $26 - $10 and we get $16. 

In order for her to rent 7 movies, makayla needs $16 more dollars.