| 1) Original Question & Solution | (Unit Five – Quadratic Functions & Equations: Skills Check, Question #5) |
| a) Original Question |  |
| b) Original Solution |  |
| c) Reflection | When I got the original solution, I was not aware that you needed to complete the square in order to find the final solution; I thought you could simply factor out the 5 and then get it into standard form but I soon discovered that it wasn’t possible because you would need a perfect square in order to get it into standard form. This was a broader conceptional error because I would have gotten the correct answer if I knew that the key component/ first step to getting the solution is to firstly start by completing the squares and not by factoring out the greatest common factor. |
| 2) Corrected Solution |  |
| a) Correct Solution | 1. The first step is complete the square; you would take 5x^2+20x (from the original question and factor out the 5 just from 5x^2+20x (not including the negative 10), so now you’re left with y=5(x^2+4x)-10.
2. Now, you need to completely complete the square; so, you would take the 2nd number factored in the bracket (in this case, 4) and multiply by ½ and then square it; (4 x ½) = 2^2 = 4. You’re now left with y=5(x^2+4x+4__)-10. 3. After, you have got to minus the value that you have just found inside the brackets as well (-4) because then it will balance it out making it equal, so that it won’t mess with the original values. Now, we’ve got y=5(x^2+4x+4-4)-10. 4. To complete the square, we have got to multiply the 5 by -4 to get it out of the bracket so we can form a perfect square; 5(x^2+4x+4)-20-10. 5. We are now able to simplify it by simplifying the numbers out of the bracket (-20-10) and forming the perfect square; we now will get the final solution, 5(x+2)^2-30. |
| 3) Core Competency Reflection | These past few mistakes as learning assignments have improved many of the core competencies; however, for this assignment specifically, my critical thinking has improved because it is needed to figure out each and every step and finding out exactly what I did wrong and finding the correct solution through each step, thoroughly by each detail; then, being able to teach it to someone by explaining my steps improved my understanding (even now). With that, I will also be analyzing my whole thought process and be able to see plenty of growth in my knowledge now. |