ARCHIVE - Reading Responses and Reflection 2 – Due 6pm Sun. Apr. 13 | Patterning the World: Connecting Mathematics and Science

The reading assignment this week is precalculus Ch 3.2 and physics Ch 2.5, 2.6, 2.7. Reading Responses are intended to help you keep up with the reading, orient you to the material for the upcoming week, and to give your instructors feedback on how best to use class time based on what you have difficulty with. You are welcome to use your books and other resources to complete the reading responses, but should take it individually. We're looking for your thoughtful effort, but this is just the beginning of our week so what you don't know after reading the texts is just as important as what you do.

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Precalculus Reading

1. The standard form of a quadratic function is f(x) = ax² + bx + c. The vertex form (also called the transformation form) of a quadratic function is f(x) = a(x - (h))² + k. Note that the a in the standard form is the same as the a in the vertex form. In the following questions use the ^ symbol to indicate a superscript, e.g. type b^2 to mean b²

1. a) Give an expression for the parameter h in terms of the parameters a, b, or c.

1. b) What does h tell you about the graph of the quadratic function?

1. c) Give an expression for the parameter k in terms of the parameters a, b, or c.

1. d) What does k tell you about the graph of the quadratic function?

1. e) What is f(0) in terms of a, b, and c?

1. f) What is f(h) in terms of a, h, and k?

2. Look at the quadratic function graphed for Exercise 1 on p. 172 to answer the following questions.

2. a) What are the coordinates of the vertex?

2. b) What is the y-intercept?

2. c) Estimate the x-intercepts (also called the roots).

3. Look at the second half of Example 2 on p. 164, from “...we can expand the formula and simplify terms:”. Look at each step of the subsequent algebra, and re-write it into your notes, filling in any missing steps that make it clearer to you. Note that the the first expression g(x) = ½ (x+2)² - 3 is really the vertex form g(x) = ½ ( x- (-2) )² + (-3) for the parabola.

3. a) Identify any steps where you have trouble following the algebra and be specific in your description (example: Between steps 3 and 4, the parenthesis disappeared and I’m not sure what happened to them). Make sure you have these in your notes also, and bring your notes to Monday's class sessions.

3. b) Evaluate g(3).

4. The discussion that begins on the bottom of p. 169 and continues through p. 170 shows how to find the x-intercepts (also called the roots) of a general quadratic function. Look at each step of this process (both algebra steps and the discussion) and re-write it into your notes, filling in any missing steps that make it clearer to you.

4. a) Identify any steps where you have trouble following the algebra and be specific in your description. (Write in your notes, bring to class)

4. b) Is the formula f(x) = a (x + b/(2a) )² + (c - b²/4a) at the bottom of p169 in

Standard form

Vertex form

Standard form using vertex form parameters

Vertex form using standard form parameters

Physics Reading

2. Consider two balls that have identical size and shape. One ball is made of lead and is about 4 times more massive than the second ball which is made of aluminum. Both balls are released from rest at the same time from shoulder height above flat ground. Neglect air resistance.

Which ball hits the ground first?

lead ball

aluminum ball

hit at the same time

Reflections

What would you like us to spend class time on from the precalculus readings?

What would you like us to spend class time on from the physics readings?

What material from the past week (or before) are you still having difficulty with? (Please do let us know, but also try to take advantage of all your resources: QuaSR, study groups, appointments with faculty, on-line tutorials & videos, etc.)

Prompt 1: Describe an instance or instances where you improved your ability to use appropriate tools strategically. Give specific examples with details. (#4)

Prompt 2: Describe an instance or instances where you improved your ability to analyze and interpet data. Give specific examples with details. (#6)

Reading Responses and Reflection 2 – Due 6pm Sun. Apr. 13

Precalculus Reading

2. Look at the quadratic function graphed for Exercise 1 on p. 172 to answer the following questions.

Physics Reading

2. Consider two balls that have identical size and shape. One ball is made of lead and is about 4 times more massive than the second ball which is made of aluminum. Both balls are released from rest at the same time from shoulder height above flat ground. Neglect air resistance.

3. A ball is launched straight up in the air starting from the ground, reaches its maximum height, and comes straight down landing back on the ground. Neglect air resistance.

Reflections