Math

Quadratic Intercept

A quadratic intercept is the point where a quadratic graph crosses the x-axis, meaning the value of y is zero, and it can be written in intercept form y = a(x - p)(x - q). It can be used to predict real-life situations such as where a rocket or a thrown ball will land.In this case study, there are several parts of the quadratic intercept form that I could improve. First, I could show my steps more clearly when finding the intercept form so it is easier to understand how I got the equation. Second, I could explain more clearly what the intercepts mean and how they relate to the points where the graph crosses the x-axis. Finally, I could improve my graph by labeling important points such as the intercepts and the vertex. These improvements would make my work clearer and show a better understanding of the quadratic intercept form

Tracker

Key Steps for Parabola Analysis in Tracker

Import Video: Open your video file (File > Open File).
Trim Video: Use the clip settings to select only the frames where the object is in motion, removing the start/end.
Calibrate Scale: Click the Calibration Tools icon, create a Calibration Stick, and SHIFT+click both ends of a known reference (like a 1m meter stick).
Set Axis: Set the axes to place the origin (0,0) at the start of the trajectory to make parabolic analysis easier.
Track Projectile: Create a new Point Mass (Track > New > Point Mass). Hold SHIFT and click the center of the object in each frame. The video will auto-advance.
Analyze Data: Right-click the data plot and select Analyze. In the Analyze window, select Curve Fits and check Parabola to see the formula and coefficients ( y = A t 2 + B t + C 𝑦 = 𝐴 𝑡 2 + 𝐵 𝑡 + 𝐶 ).
Interpret Data: The parabola fits the y 𝑦 -position vs. time graph, where the coefficient A 𝐴 relates to acceleration due to gravity ( A = 1 2 g 𝐴 = 1 2 𝑔 ).

Analysis:

Click on the "Data Tool" icon.

Inside the data table, select the column to plot vertical position vs. time.

Select Analyze > Curve Fits and choose "Parabola" from the menu.

You will get the equation of the Parabola from Tracker

I connected my parabola analysis work with what we learned in a previous math class. In that class, we also studied quadratic equations and practiced finding parabolas, but with simpler examples on paper. This project was similar, but more advanced because I used Tracker to analyze a real rocket video and find the equation of its path. This helped me see how the math we learned before can be used in a real experiment.

Paper Rocket

Form the Body: Cut a narrow strip of paper (approx. 5 inches long) and roll it tightly around a pencil to create a cylinder. Tape the seam of the tube.
Create the Nose Cone: Seal one end of the tube to make it airtight. You can do this by folding the end over and taping it, or by twisting the end into a point and taping it.
Add Fins: Cut out small triangle-shaped fins and tape them to the opposite end of the cylinder (the open end).
Launch: Insert a drinking straw into the open end of the tube, aim it safely, and blow hard to launch the rocket.

My paper rocket project connects to the global issue of improving rocket and transportation technology. In this project, I built a paper rocket, we launched it by a straw, and recorded the results of each launch. This process is kind of similar to how engineers test their rocket designs and collect data to know how rockets fly. By changing parts of the rocket, such as the cone part or the fins, by observing the data in the tracker, i can know the relationship between the number of fins, the cone, the distance, and height. A possible way to solve this problem is by testing rockets many times, recording the results, and improving the design each time. By doing this, engineers can make rockets safer and work better. This small experiment shows how testing and studying results can help people improve technology in the real world.

Finding The Equation

My portfolio work connects to the local issue of improving science education in Taiwan. In this activity, we record a paper rocket launch and use the software Tracker to set coordinates and study the rocket’s path. And then we use the data points to find the quadratic equation that represents the rocket’s flight. This activity shows how math can be used to understand real movement. A possible way to improve this issue is that if students in Taiwan learn to use tools like Tracker and apply math to real experiments, they might become more interested in science and better understand how math is used in the real world.

how i apply my experience to this assignment

When working on my project about Angry Birds and projectile motion I was able to show that this was true by using actual data from another assignment for this class which had to do with quadratic functions and graphing parabolas (the previous assignment was already done at last semester of grade 8). In one of the assignments that I completed late in grade 8, I did some work to create an equation for a parabola and to find the vertex of a parabola, along with finding the line of symmetry for that parabola. Because I had some experience with creating and manipulating graphs for prior assignments I was able to create a graph showing the birds flight path after being shot and how far away thebird is from the target. I showed not only an understanding of how changing a variable's value will affect the way the parabola looks but I also created a graph representing how each variable's change has affected the way the parabola looks when the variables are changed at the same time.

using quadratic to solve angry bird porblem

I made a curve parabola for my Angry Birds model based on the quadratic function that was used to plot the path of each bird. I change how the bird move include height and distance in order to land on the desired target. This actually presented more difficulty than just a usual graph because I needed to modify the equation for each bird and test multiple variations to find the best equation to hit the target. Additionally, I had to ensure my graph aligned with the position of the target, to maintain an accurate graph. As such, I can apply quadratic functions to solve real-life problems involving projectile motion, by keep improving this skill i believe it can be very useful in the future.

understanding quadratic funtions in my project

Using quadratic equations, I modeled the flight paths of the Angry Birds shown on the worksheet. The zeros for each flight path give the x intercept where each bird begins and ends, and the vertex for each of the paths gives the maximum height of the bird during that flight. The axis of symmetry gives the mid-point of the flight path, and by adjusting the quadratic equations to match the graph, I could observe how changing the values in the equations changed the shape of the parabola. This project has shown me that I can use quadratic functions to address a variety of real-life situations and I have a better understanding of how to use the function to solve for real life examples.

TRIGoNOMTRY COMIC

Class-specific 2: Application & Problem Solving

This work was based on a series of things that happened in a specific place. I chose a park, and with this choice came 6 questions that I had to draw out and solve. This assignment helped us practice applying real world situations into math problems and solving them using the skills we learned in class. Through this process, I was able to use math better and improve my understanding of this topic. Overall, this assignment used a unique way to help me gain a better understanding of the topic, and it not only challenged my math skills but also challenged my creativity.

Class-specific 3: Mathematical Communication

In this assignment, I used Mathematical Communication by explaining math problems to my classmates and teaching them how to solve the problems step by step. I also explained my thinking to my friends to check if I truly understood the topic myself. By using these strategies, I gained better knowledge related to math and also made sure that I really understood the problems.

Growth: Work/ Study Habits

Back in last semester, I did not really focus in math class. I would usually just hang out with my friends and play video games throughout the class. However, as the questions and lessons started getting harder and harder, I began putting more effort into learning math. I found it kind of fun when the questions were challenging but still possible for me to solve. This is the most significant improvement in my learning habits based on my personal experience.

Unit 8 Quiz

Growth: Collaboration/ Feedback

I worked with my classmates by reviewing together before the test and helping each other correct wrong answers after the test. We shared where we got mistakes and analyzed what type of mistake it was, like if it was caused by being careless or because we did not review that part enough. I think these are very important things for people to improve and learn math faster. This way of learning honestly helped me a lot and made me understand my mistakes better.

Growth: Connection to Future Plans

This assignment helped my future plans by improving my math basics. In the future, I would like to learn topics related to math and business, such as calculus, statistics, and microeconomics. These subjects require stronger math skills, which makes this trigonometry assignment more important when I think about both the present and the future. Overall, this assignment helped my future plans by making my math foundation stronger.

Class-specific 1: Conceptual Understanding of Mathematics

In my Unit 8 math project, I solved different types of triangles using both the Law of Cosine and the Law of Sine. I learned when to use each formula rather than just memorizing them. Although I made a few errors with my calculator that caused me to lose points, the majority of my work and thought process were accurate, which demonstrated my understanding of this topic.

Page updated

Report abuse