The variables “a”, “h”, and “k” all have their own effect on the parabola. They all come from the equation shown in figure 2. The “a” value determines if the parabola opens upwards, downwards or if it’s narrow or wide. Since a is positive and greater than 0, a=3, the parabola is narrow and opens upwards. The “h” value determines if the parabola shifts to the left or right on the “x” axis. If “h” is negative, it will shift right, if “h” is positive the parabola will shift left. Since h is -4 the “x” value of the parabola will be 4, shifting to the right and the “x” value of the vertex will be 4. The “k” value decides if the parabola will shift up or down. The “k” value is 2 meaning it will shift up. Additionally, the “y” value of the vertex will be 2, vertex = (4,2).  

Self-Assessment

1. I portrayed the same mathematical idea through my graph, paragraph, and equation. For example, I explained the “a”, “k”, and “h” values in my paragraph, and they, additionally, have visual aids through the graph and the equation.
2. I used mathematical vocabulary multiple times throughout this assignment. For example, when explaining what the “h” and “k” values do, I used phrases like shifts right or left on the “x” axis or shifts up or down on the “y” axis to explain my point.
3. I used the website Desmos to graph my two parabolas in a neat and tidy way. After, I found a scale that made it easy to differentiate my parabolas and took a screenshot leaving just the graph, none of the unnecessary border.