Reflection on Quadratics
During the quadratics unit, I learned a great deal. Using my past knowledge and the things we were taught, I was able to better understand how numbers work together to solve for various things. This unit has taught me many things which will surely be extremely helpful for me in the remainder of my educational career. To summarize all the things I learned,
Firstly, in the factored form part of the unit, we first learned how to multiply binomials and went through a special products investigation. Next, we learned about common factors and simple grouping. We then went on to factoring trinomials with an a value of 1, and later factoring trinomials with an a values that is not 1. We next went on to factoring special trinomials and the different types of factoring. We then learned to solve by factoring and finally to graph by factoring.
Secondly, in the standard form part, we first learned to complete the square to get vertex form, and we next learned to solve for x using the vertex form. Then we learned how to use the quadratic formula to solve for x intercepts and finally learned to apply the quadratic formula for word problems.
Lastly, in the vertex form part, we first learned how to use tables of values, first differences and technology to identify the vertex and axis of symmetry for a parabola. Then we analyzed equations of parabolas in vertex form to learn what the equation says about the parabola. We then learned how to create equations for parabolas when given the transformations. Next we learned how to graph a parabola using only its equation in vertex form. And finally, we learned to find the equation of the parabola using only the graph of the parabola.
In conclusion, the quadratics unit had better prepared me to solve the various predicaments which I will most likely face when I go onto higher levels of education, and also in everyday life situations. Therefore I am glad I learned the concepts taught in this unit.
First off, I can connect the vertex form unit to graphing parabolas because all the variables used in vertex form affect the parabola in different ways and will determine the way in which the parabola appears.
Secondly, I can also connect the standard form unit to graphing parabolas because when you use the quadratic formula, you are able to find the x intercepts of the parabola along with the vertex, which will allow you to graph the parabola with ease.
Finally, factored form connects to graphing because when you factor the expression, you receive the x intercepts, and then when you sub in the average between the intercepts (if x intercepts are 4 and 8, 6 is the average) and sub that in as the x value, you get the vertex of the parabola. Now that you have these three points, you are able to graph the parabola.