 This video is going to talk about quadratic applications. So we have a height of an object thrown upward from the roof of a building 408 feet tall with the initial velocity of 96 feet per second and it's given by this equation. Thankfully they give that to us. Where h of t represents the height of the object after t seconds. How long will it take the object to hit the ground? So we have this object here that's being thrown and when it hits the ground it's going to look something like this. It's going to go up in the air and come back down and hit the ground and when it hits the ground the height is equal to zero feet because it's on the ground. So we really want to know when this is zero is equal to negative 16 t squared sorry about the bleed here plus 96 t plus 408. So let's try putting that in our calculator. We have lots of ways that we know how to solve it from previous video. So negative 16 x squared plus 96 x plus 408. So I have my y2 equals zero I can now graph but I need to change my window because I have a standard window and this constant that's the y-intercept is at 408. So I need to change that and I've already done this. I'm saying that but the max is 20 that's 20 seconds. I think it's going to take probably less than 20 seconds for this thing to fall. But I needed to go up to something bigger than 408 because that's where it's starting. So I chose to say 600 feet. X is in seconds so 20 seconds this is 600 feet and when I graph I get this nice graph. Obviously I didn't need as much as 20 but this is a good graph. I want to know this point right down here. So I need to intersect. I already have the y2 equals zero which is the value I want the height to be. So I do intersect which is five and I just have to press enter enter enter because I'm already on that side of my graph and it tells me that t is equal to 8.87 approximately seconds. When it hits the ground it takes 8.87 seconds to get there. Cost to produce bottled spring water is given by the cost equation. C is equal to that's a 16x plus I mean 63 where x is the number of bottles in thousands and then total revenue from the sales of these bottles is given by this equation. So determine the profit equation. Well profit is revenue which is negative x squared plus 326x minus 18,463 minus the cost equation which is 16x plus 63. But remember this is going to be now minus 16x and minus 63. Negative x squared stays but 326 minus the 16x of both x's gives me plus 310x. I know I could have done that in my head. And then negative 18,463 minus 63 more gives me minus 18,526 so that's my new equation. So it says after a bad flood contaminates drinking water when you're by community the owner decides to bottle and donate as many bottles of water as it can without taking a loss. This means they break even. Approximately how many bottles will they produce for the flood victims? That means that their revenue is equal to their cost. Let's think about it this way. Revenue is equal to cost or we could say that profit is equal to zero since we already have that nice equation. So zero is equal to negative x squared plus 310x minus 18,526. Well we could graph it, that would be a way to find the solution or let's try another method this time. When it's equal to zero we can also use the quadratic formula. So we know that a is negative 1, b is 310, and c is that negative 18,526. So program quadratic 84, quad 84, enter again and we have negative 1, enter 310, enter and then negative 18,526 and it tells us that x is going to be equal to 80.84 or and whichever would you choose 229.16 if we round it. How many approximately would they produce? We would want to say then that they're going to have the 229.16000 bottles because remember it was in thousands.