My equation:

The parent function:

The significance of a, h and k

The a determines whether the graph is downward or upward and the width of the graph. The a in my parabola is a negative number, so unlike the parent function, the parabola is downward. If a is positive, the parabola open upward. Furthermore, as the a value of a increase, the width of the parabola narrower. Also, since the value of a in this parabola is small, the width of the parabola is wider than the parent function. h and k represent the vertex, the vertex can be shown as (h,k)=(5,-5). Also, corresponding to the value of h, the graph moves horizontally in the positive direction by 5, and corresponding to the value of k, the graph moves vertically in the negative direction by 5. a,h,k changed this parabola at the vertex, intercept, range and shape.

Self-Assessment

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

Mathematical ideas were represented in multiple ways by shifting parabolas using mathematical formulas and Desmos. The parent function was also shown to clarify the meaning of each of a, h, and k, and to show how the parabola can be graphed.

2. State the relevant mathematical vocabulary words you used to demonstrate your understanding?

vertex, x and y intercept, range and shape

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

I organized the information using headings, screenshots, and graphs utilizing desmos. I also color-coded the graphs to make it easier to tell the difference between the parent function and my graph, and clearly marked the vertices.