Category / Math 11

by Jordyn

Transforming Parabolas

GRAPH:

Graph A (RED): Quadratic parent function f(x) = x^2

Graph B (BLUE): Opens up and is wider than the parent function f(x) = 1/5x^2

Graph C (GREEN): Opens down and is narrower than the parent function f(x) = -4x^2 + 5

Graph D (ORANGE): Parabola that is shifted to the right of the parent function f(x) = 2/5(x-6)^2 + 2

Graph E (PURPLE): Parabola that is shifted lower than the parent function f(x) = 1/2(x-6)^2 – 2

PARAGRAPH

In my equations, the variables a, h, and k change the width, the position of x, and the position of y. The example I will be using is f(x) = 2/5(x-6)^2 + 2, which is Graph D in this assignment. In this equation, +2/5 describes how wide the parabola will be and how the parabola will open up. In this equation since +2/5 is a positive fraction, the parabola will open upwards compared to another equation, like f(x) = -4x^2 + 5, where the a is a negative number. -6 is the h in this equation and it describes where the parabola will be placed horizontally on the graph. Since the equation is f(x) = a(x-h)^2 + k, the h being a negative means that the number we are using is positive, so the x on the vertex will be +6. The k is +2, and it describes where the parabola will be placed vertically on the graph. Since the k is a +2, the parabola will be shifted to the right 2 times. If the k was a negative, it would have been shifted left 2 times.

SELF-ASSESSMENT

I was able to show the main mathematical idea multiple times by using the same equation but changing the values each time. In the equation f(x) = a(x-h)^2 + k, changing each variable changes the position, width and direction that the parabola is going in. Being able to the use the same formula while changing the parabolas is useful to keep the same mathematical idea throughout the assignment. Some vocabulary I used while showing my understanding include vertex, parabola, positive, negative, horizontally, and vertically. I used the formatting to show and label each point on the graph using bold colors and words. I was also able to show the numbers on the graph going up from one so it looks organized. Lastly, I removed minor guidelines to make the graph look neater.

by Jordyn

Reviewing Chapter 1: Factoring & Radicals

  • The part of chapter 1 I am most comfortable with is factoring trinomials, perfect squares and difference of squares. I am most comfortable with these because they are the concept I am most familiar with and I understand the most about what steps I need to take to solve these accurately.
  • The most difficult part of chapter 1 for me is dividing radicals, more specifically using quotient property. This is the most difficult because I often struggle with figuring out what needs to be moved and what I need to simplify in these equations.
  • I usually learn new material the best when I am taught the material in class (with examples) and then given a chance to try it out afterwards. For example, when we get to do whiteboard work after learning something new or getting workbook questions to practice my newfound skills.
  • I plan to prepare for the unit test by completing the given workbook questions, looking over notes I don’t understand as well, and using the extra practice to improve on what I already know. This will help me to understand the chapter enough so that I don’t have to worry about certain topics on the test.
  • I have completed all of the practice problems other than the review questions we got introduced to on Monday. I plan to do these in preparation for the test on Wednesday.
  • The statement “I persevere with challenging tasks and take ownership of my goals, learning and behavior.” means that I can work independently and work towards solving my problems by taking ownership of my learning. I can work towards understanding a concept fully without many struggles and can enhance my learning by taking on challenging tasks.