Graph red (parent function): f(x)=x^2

Graph blue: opens up and is wider f(x)=1/5x^2+6

Graph green: opens down and is narrower f(x)=-3x^2-4

Graph purple: shifted right f(x)=(x-5)^2-2

Graph black: shifted left f(x)=(x+4)^2-5

In my equations, it shows that changing the a, h and k in a quadratic equations in vertex form have different effect on the parabola. For example, in graph blue and graph green, it shows that as a gets smaller, the parabola opens wider and it opens narrower when a is bigger. Also, these two graphs show that if a is positive, the parabola opens up and it opens down when a is negative. The vertex of the parabola depends on h and k. From graph black and graph purple, it shows that by changing the h of the function, we can shift the parabola to the left or to the right. if h is positive, the parabola is shifted left and if h is negative, the parabola would be shifted to the right. So the x value of the parabola’s vertex is decided by h.From all the four graphs, we can learn that the k in the function depends the y value of the vertex. In conclusion, the vertex of the parabola can be written as (-h,k).

Self Assessment:

1: How did you represent the same mathematical idea in multiple ways in this assignment?

I represent the same mathematical idea in multiple ways by showing the parabolas in both forms of functions and graphs.

2: State some of the relevant mathematical vocabulary words you used to demonstrate your understanding.

Vertex, function, parabola, positive/negative, quadratic equation

3: How did you use formatting to share your information in a clear and organized way?

I coloured the parabolas in different colours so that it is more clear and easy yo separate them. Also, I showed the parabolas’ vertex in the graph so that it is easier for me to show the relationship between a, h, k and the vertex of the parabola.