Here I used the quadratic expression to find the X- intercepts. I went step by step to be able to find the exact X- intercepts I needed.
Here to find the vertex I added the x intercept together and divided the answer by two so I could find the middle point.
Once I had found the middle point I pluged into (T) and I solved for the equation to find the highest point. And i found the vertex of (2.875,292.25)
Problem Statement: The Manchester United soccer team has taken the championship with a score of 3-2. The club wants to celebrate, to celebrate club will be putting on a fireworks display. The fireworks will be red and will, be launched from the top of the London tower. The manager of the club isn't concern about the price but wants to know the timing of the mechanism that detonates the fireworks and he's also concerned about the players safety.
List Of Questions To Help Set Up This Problem What is the unknown peak of the fireworks ?
What is the unknow distance it will travle ?
What degree angle was the firework launched at ?
Peak Of When Fireworks Will Explode. The way I found the peak (VERTEX) is I used the quadratic expression to find the X-intercepts, after I had found the X-intercepts I had to find the vertex (PEAK) to find the vertex what you due is you take bothe of the X-intercepts and you divide them by two. One I divided the X-intercepts by two , by doing so I found the middle point , after finding the middle point I pluged it in two (T) and I solved the equation to find the highest point . So I was able to fid the vertex (PEAK) of (2.875,292.25)
Where The Fireworks Will Land. To find how long did the fireworks traveled you first have to know how long it took for it to land so you use the equations d(t)= 92t tan 65. You plug in (7.15) which is the time it took for it to travel. You plug it into (T) And than you solve for it and that's how you find the distance it traveled.
Problem Evaluation honestly at first I did not like the problem , I think it was because when Mr.C was explaining to us the problem I felt like it was going to be a bit confusing but as time went by I started learning a bunch of new things and I started to understand what we were doing and I started liking the topic because I felt more and more confident every day. By this time I really like the problem I understand it and I feel comfortable when I am explaining it. I learned many new thing like multiplying binomials how to find the X,Y Intercepts, The vertex how to use the 2 types of forms. Standard and vertex form. I learned how to use the really long quadratic expression. So every time I learned how to do something new I each time started to like the topic more and more until I felt very comfortable about it.
Self Evaluation If I were to grade myself for this portion of the semester I would give me a solid A because I worked really hard and I tried my hardest in each test , each assignment that we would get. I would ask questions if I was stuck I would do all my homeworks and I would share all my ideas that I had when it came to talking to my group or to the whole class. I feel i've done a really good job this semester I am really proud of myself for all the work i've got done and all the heart I put into the work I got done.