“A” determines the direction and width of the parabola. If “a” is positive, the parabola opens upwards, and if it’s negative, it opens downwards. Because of this, in my purple parabola I used -4. To make the parabola more narrow than the parent function, in this case it had to be represented by a number greater than 1 (>1) or less than -1 (<-1) so I chose 4. “H” represents the horizontal shift of the parabola, moving it left or right along the x-axis. For the green parabola with the vertex (7,0) I used positive “h” to move it to the right. The ”k” must be used to move the parabola up or down along the y-axis and in the case of my blue parabola I used a negative “k” to ensure that it is shifted down lower than the parent function. Finally, in the orange parabola I chose a positive “a” to make it open up and I chose a number between 0 and 1 (0<a<1) to ensure that it is wider than the parent function. 

1) I represented the same mathematical idea in multiple ways through visual representations, like using graphs. Another way is through symbolic representations, such as using equations or formulas. And finally I think with verbal representations, explaining in my paragraph the ideas I had for moving the parables. By exploring different ways to represent a mathematical idea, we can gain a deeper understanding and find different approaches to tackle problems.

2) To demonstrate my understanding I used mathematical vocabulary words like “vertex” that is the point of intersection of the parabola and the axis of symmetry, “parent function” that means the simplest function of a family of functions. The “axis of symmetry” is a line that divides an object into two equal halves and finally we have the x.intercept that is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. 

3) To share my information in a clear and organized way I followed the advices that Ms Lam gave to us such as adjusting the settings on Desmos with a step of 1 for x and y and I got rid of minor gridlines. I also tried to change the expressions of the parabolas so that they are as detached as possible and with different vertices to make them more visible. 

• The part of chapter 1 that I am most comfortable with is the factoring one therefore up to point 1.2b
•   The most difficult part of chapter 1 for me is 1.7 because many things mix together and sometimes I struggle to recognize all the steps I have to do
•   I usually learn new material better by paying attention to the explanation but above all during group work. I think it’s a good time to compare myself with people like me who can always help me when I need it and if we don’t understand something, the teacher is there. I think it’s a good moment also because it’s something that happens immediately after the explanation and this lets me know if I have correctly understood what was told to me shortly before
•   I plan to prepare for the unit test by first reviewing the theory and the notes on teams and the exercises I have already done. Then I will go to the “extra practice” section and do those exercises too, checking that my results are correct. I’ll probably do them all or until I feel confident enough.
• I have already completed all the assigned practice problems in class or during flex time.
• The statement: “I persevere with challenging tasks and take ownership of my goals, learning and behavior” means a lot to me and I think it fully describes my educational journey. Especially for the precalculus class. I am of the opinion that it is important to always practice and complete the tasks assigned to us. We must not ignore the most difficult problems and it is precisely by making mistakes that we learn, only in this way can we truly improve. Being in grade 11 I think I am old enough to be able to manage my work on my own and after the teacher’s explanation I know that it is up to me to practice enough to achieve good results. Obviously I am also at an age where I have to manage my behavior such as using the phone in class only when it is required and not talking over others.