By: Jasmeen Mann
To start off with, in this chapterwe have learned a lot of graphing by different equations. As we did vertex form we learned about the differences between Maximum and Minimum values. Every time we solve an equation, we would see if it would open up or down. So if the equation was positive the graph opened up, but if it was negative then down. The main thing that affects graphing is this formula: y=a(x-h)^2+k. This is because “a” tells the direction of the opening and compression or stretch. If the a-value is greater than 0, there will be a vertical stretch, which will cause the parabola to look thin and if the a-value is less than 0, there will be a vertical compression, which will cause the parabola to look wider. Note that the a-value will affect the y-values of the parabola tells us the horizontal translation and k vertical translation. So if “a” is positive then opens up, but if negative then down.If H/V is positive then the graph is on the right but if negative then on the left. Even when we did the second unit, everything will matter on the equation. So the equation was y=(x-r)(x-s), in which r and s give you the x-intercepts and using the knowledge from before you would graph it. The r value was basic h because if r was positive in the bracket it would be negative outside in which will be on the left said when graphing. Lastly, in standard form the main formula was: y=ax^2+bx+c. In which “a” would give you the shape and directions. The c vale is the y- intercept. By using our knowledge from the other two units when we complete the square, which is basic adding and subtracting a constant to create a perfect square trinomial within the equation. I feel I did the best in this unit, this is because I got 100% on the test only because I understood completing the square and how to graph it. I feel like from vertex and factoring; standard form was the easy for me. This is because it was more like we had to apply the knowledge from before, in which I got really good at that. The biggest connection between the equation or the method and graphing is, that the graph will be affect when the values are positive or negative. This is because this either will affect the a, h, k, r, s value and showing the direction or where the graph should be. In this unit everything matter on if the equation is solve right then the graph is right. Even if you make a small mistake then the graph is wrong. For instance if you forget to change the h value because it’s the opposite the whole graph is wrong. My strength in these units was the knowledge part, I was able to complete the equation with no problem. But, my weakness was either graphing or the word problem because I had to apply new things to it. To conclude, the main connection between graph and the units is that the value of the equation will give you the graph needed.