If a basketball player shoots a foul shot releasing the ball at a 45° angle from a position 6 feet above the floor, then the path of the ball can be modeled by the quadratic function H of X equalling -40 four X ^2 / v ^2 + X + 6, where H is the height of the ball above the floor, X is the forward distance of the ball in front of the foul line, and V is the initial velocity with which the ball is shot in feet per second. Suppose a player shoots a ball with an initial velocity of 24 feet per second. Now answer the following questions. So when we look at this, the part A is given as determine the height of the ball after it's traveled 5 feet in front of the foul line. So the five is going to represent the X. So we're saying H of five. We want the height when we're five feet in front of the foul line. So -44 * 5 over the velocity. Well, that's given to us right here. The initial velocity is 24, so we're going to put in 24 and square it. Then the plus X, the X again is the five, and then +6. If we put that into a calculator, we are going to oh, this was 5 ^2 up here, sorry. So -44 * 5 ^2 / 24 ^2 + 5 + 6. When we plug that into our calculator, we get approximately 9.09 I rounded to two decimal places. Part B is asking the same kind of question. Determine the height of the ball after it's traveled 12 feet in front. So instead of H of five, now we want H of 12. So we're going to have -44 * 12 ^2 / 24 ^2 + 12 + 6. Once again, we're going to put it in our calculator and we get about 7 rounding to two decimal places. Now these are actually representative points. This is saying when the X is five, the Y is 9.09. This next one when X is 12, the Y is 7. So with part C, it says find some additional points and then graph SO59 point O 9. When I look at my scale, it's going by up to 25 for the axis. So I can see we're counting by fives 51015202551015. So I want to figure out a 59 point O 9 here. 5 this Y is being counted by fives 5/10/15. So that's obviously 5 is less than five here. So that one's not going to be right. Here's 5 and this is a little bit less than 10, so maybe that one's OK. Here's 5 and this is over 10. So that's definitely not going to be the case. And here's 5 and it's almost zero. So that one's not the case either. So B is the only one just looking at one point that makes any sense. Let's see if the point 12 seven's on here. So 510, little bit past 10, if we go up here, we can see that it's above the five line but below the 10. So letter B was the one that makes some sense. Continuing on looking at part D&E, Part D says the center of the hoop is 10 feet above the floor and 15 in front of the foul line. Will the ball go through the hoop? So now we just want to know is this going to be a true statement or not? So if it's going to be 10 above the floor are H of X is 10 and 15 feet in front of the foul line. So this once again is really a point. It's the point 15, 10. So we have 10 equaling -44 * 15 ^2 / 24 ^2 + 15 + 6. If this is a true statement, we're going to say yes, it's OK, and if it's not a true statement, we're going to say no. And it doesn't turn out to be a true statement when we compute it. So the last question says, if not, what does the initial velocity have to be? So now instead of the 24, we're going to say we don't know what that value is and we're going to solve it. So -4415 ^2 over v ^2 + 15 + 6. The 15 and six is 21. I'm going to subtract it to the other side. So I'm going to get -11 equaling -44 * 225 / v ^2. I want V so I'm going to cross multiply -11 V squared equal -44 * 225, divide and square root and we can see V equal 30.