Over the weekend, please complete the following problems from the attached worksheet: 10 – 15, 17, 20.
This is just practice for Completing the Square. On Monday we will complete the square together in class using the Standard Form of a Parabola: y = Ax^2 + Bx + C.
Today in class we discussed strategies for solving quadratic equations when A is not equal to 1.Tonight, please pick 6 of these equations to solve with completing the square. Check your work by typing “solve” on your calculator!
Today in class we began our study of Completing the Square. Please pick 8 of these problems to solve tonight for homework. Everyone should do #27.
1. An athlete throws a shot put with an initial velocity of 40 ft per second. At the point of release, the ball is 6.5 feet from the ground.
- Write an equation that models the height h in feet of the shot put as a function the time t (in seconds) after it was thrown?
- Use the equation to find the time that the shot put is in the air.
- How long will it take the shot put to reach it’s maximum height? What is that height?
2. An object is launched at 19.6 meters per second (m/s) from a 58.8-meter tall platform.
- Write an equation to model the height (in meters) over time (in seconds).
- When does the object hit the ground?
3. Ralph dropped a tennis ball from the top of Marie Murphy school, which is approximately 30 feet tall.
- Write an equation to model the situation. (hint: What is the initial velocity?)
- How long will it take for the ball to hit the ground?
4. Ophelia THREW a tennis ball upwards from the top of Marie Murphy.
- If the ball was in the air for about 2 seconds, how fast did she throw it?
- What is the highest point the ball reached before falling back to the ground?
Tonight, please complete the following projectile motion problems from your textbook:
9.7) 46 – 49
10.3) 50, 52, 53, 54.
Try to factor every problem WITHOUT a calculator. Sometimes the book creates problems which CAN’T be factored. When that is the case, then you may use a different strategy.
Over the weekend, you will not have any math homework. Upon further review, it was determined that we needed a little more prior knowledge before working independently on Projectile Motion Problems.
If you are looking for some cool math over the weekend, create some random equations for parabolas in Standard Form, and look for relationships between the (A) value in the equation and the Change in the Rate of Change that we learned about in class today.
This is a great exercise in Mathematical Practice 7.
The “Big Bertha” model rocket, produced by Estes, reaches a maximum height of 500 ft. (This is all true and accurate)
It’s height over time can be modeled by the equation: y = -16x^2 + 176x
x: time in seconds
(the ^2 means “x squared”, but I can’t type that on the blog.)
Using everything you know about Algebra, with some help from your calculator, please write thoughtful responses to the following questions over the weekend:
1. Make a graph and table for this equation. Don’t forget to keep in mind what the variables represent.
2. How high off of the ground is the rocket before it is launched? How do you know?
3. How long does it take the rocket to reach it’s maximum height? How did you find it?
4. What is the total time the rocket will be in the air?
5. Do you notice any patterns in the table? Write down all of them, and be as specific as possible.
You should also complete Geometry Practice IV on Study Island this weekend.
Graph 10 parabolas from problems 15 – 26.
For each graph you must:
- Clearly label the key points: vertex, y-intercept, x-intercept(s), axis of symmetry
- If you can’t factor and find the x-intercepts, explain why. Use logic and reasoning to support your opinion.
Tonight, please graph all 6 of these parabolas. Then identify their key features clearly on each graph. The key features include: x-intercept(s), y-intercept, vertex, and axis of symmetry. (We sketch that as a dotted line)
As you are working on these graphs please think about when is it easier/harder to find the different features… that will be the focus of our conversations in class tomorrow.
1. y = 2(x + 3)^2 – 4
2. y = -1(x – 3)^2 – 5
3. y = 1x^2 + 7x + 12
4. y = 2x^2 – 3x – 35
5. y = 1(x – 3)(x + 3)
6. y = -3(x + 1)(x + 4)
Today in class we looked for connections between the graphs and equations of Parabolas.
Towards the end of class, Lilly noticed a connection between the equation y = A(x – j)^2 + k and the vertex of the parabola.
1. Create 6 new equations in this form.
2. Identify the vertex of each parabola.
3. Do you see a connection between the location of the vertex and the parabola? If so, what is it? Be specific!
4. Can you prove, beyond using examples, what the connection is? Do it!