1. The parent function f(x) = x²
The parent function is the original quadratic equation. It opens upward has a vertex at (0, 0). There are no transformations because a = 1, h = 0 and k = 0. All other parabolas are transformations of this base graph.
2. A parabola that demonstrates a vertical shift up
When the k value is positive in the equation the parabola moves upward on the y-axis. The vertex changes from (0, 0) to (0, 4). The shape, direction and width of the parabola stay the same because a and h do not change.
3. A parabola that demonstrates a vertical shift down
When the k value is negative in the equation the parabola moves downward on the y-axis. The vertex becomes (0, –5). The size and direction of the parabola stay the same but it is moved lower on the graph.
4. A parabola that demonstrates a horizontal shift left
The parabola moves to the left. The vertex is (–10, 0). The sign inside the brackets of the equation is opposite to the direction it moves on the x axis. The parabola keeps its original shape.
5. A parabola that demonstrates a horizontal shift right
The parabola moves to the right. The vertex is (10, 0). The sign inside the brackets of the equation is opposite to the direction it moves on the x axis and the parabola keeps its original shape.
6. A parabola that demonstrates vertical stretch
When the a value is greater than 1 in the equation the parabola becomes narrower. This is called vertical stretch. This happens because each y value increases faster stretching the parabola away from the x axis making it look more narrow. For my parabola I have a = 9 which makes for a very narrow parabola.
7. A parabola that demonstrates vertical compression
If the a value is between 0 and 1 the parabola becomes wider. This is called a vertical compression. The graph flattens because each y value grows more slowly squishing the parabola toward the x-axis making it look more wide. For my parabola I have a = 0.05 making a very wide parabola.
8. A parabola that is reflected on the x-axis
When the a value is negative the parabola is reflected over the x axis. This reflection flips the graph upside down changing its direction from opening upward to opening downward while keeping the same width and vertex position. For my parabola I have a = -0.5 which makes the parabola open downward as the a value is negative.
Communication Core Competency Reflection
I can understand and share information in a clear, organized way:
I did this by making my explanations for each parabola clear and easy to follow. I kept my answers concise but included all the important information so they made sense. I also organized my work carefully to show each step clearly and make it simple to understand how I got my results.
I think about what I am going to convey and to whom I will convey it to:
I showed this through paying attention to grammar and how I wrote my answers. I tried to explain my ideas in a way that my teacher and peers could easily understand. I made sure that my writing sounded clear and understanding so any person reading it would be able to follow my thinking and understand what I try to explain.