Parabola 1 (Red): Quadratic parent function

Parabola 2(Blue): Opens up and is wider

Parabola 3 (Green): Opens down and is more narrow

Parabola 4 (Purple): Shifted right

Parabola 5 (Black): Shifted down

In parabolas, a, h, and k, have a significant effect on the way she shape looks and where it appears on the graph. This is evident on my graph in all of my parabolas. For example, In my second parabola, (the blue one), the a value is positive and is a fraction which makes the parabola open up and wider than the parent function. There is no h and k in this equation therefore this makes the vertex (0,0) as the parabola does not shift up, down, left or right. In the third parabola (green), the vertex is also (0,0) for the same reason as there is no h or k in the equation and the parabola does not shift. However, there is an a value in this equation which makes the parabola open down and be narrow as it is a negative whole number. In the fourth parabola (purple), the vertex is (15,12). This means the h is 15 which causes the parabola to shift to the right and the k is 12 which makes the parabola start up higher as it’s minimum value is 12. This parabola has an a value of 1/5 which is a positive fraction and makes the parabola open up and wide. My last parabola (black) has no h value and therefore does not shift on the x-axis. However, it does have a k value of -6 causing the parabola to start opening from below 0 and shifts the parabola down the y-axis. This parabola is also effected by its a value which is -1/2. This value is negative which makes the parabola open down. It is also a fraction which makes the parabola open wide. In conclusion, the values a, h, and k, drastically effect the shape of the parabola and can also help us predict a parabolas shape just from the equation. This also makes it easier to check your work when solving and plotting points on a graph.

1. In this assignment, I represented the same mathematical idea in multiple ways as I showed how the different letters effect multiple equations by changing their values and adding more changes to the equations. For example, in the last equation, I made it be shifted down from the parent function and then I added a value for a which made the parabola open up as well.
2. To demonstrate my understanding, I used lots of vocabulary and terms that relate to the mathematical concepts. Some of these terms include parabola, shape, shift, y-axis, x-axis, opening up/down, values, equation, points, fraction, minimum value, etc.
3. I was able to use formatting to share my information in a clear and organized way as I adjusted the settings in desmos, like changing the steps, thickness, labelling, and choosing colours. I also took pictures of my equations so they would be clear and easy to see.