The image below shows two parabolas. The Blue parabola represents the parent function. The Red parabola is my own function.

What is a, h, and k? How does it affect my parabola?

The values a, h, and k can be found in the equation y=a(x+h)^2 +k.

How “a” affects my parabola and what it means. “a” is the coefficient at the beginning of the function that controls how stretched or compressed the parabola is. If “a” is bigger than one then the parabola will become compressed as when “a” is smaller than one or a fraction it means it’s going to be stretched out. It also represents if it becomes reflected. If the “a” is negative then it parabola will become reflected. In the case of my function the “a” is bigger than one so it became more compressed than the parent function. It is also a negative, therefore it became reflected.

How “h” affects my parabola and what it means. “h” represents how the parabola shifts but in a horizontal way. If the “h” is positive in the function then that means the parabola shifts to the left, while if the “h” is negative in the function that means it shifts to the right. The “h” also represents the “x” point of the vertex. My parabola is shifted to the left because the “h” value is positive and that is how it affects my parabola.

Lastly, the “k” value. The “k” represents how the parabola is shifted vertically. This means that if the “k” is positive then the parabola is shifted upwards while if the “k” is negative then it’s shifted downwards. The “k” also represents the “y” point of the vertex. In my function the “k” is negative and that’s why my parabola is under the x-axis since it shifted downwards, unlike the parent function.

Self – Assessment

1. How did you represent the same mathematical idea in multiple ways in this assignment? The same mathematical idea that I represented in many ways was the “a, h, and, k” values. The way I represented these was in two ways. The first one was in my own parabola so in graph form, where the “a” is -2, the “h” is +5, and lastly the “k” is -2. I also represented the values in words by having to explain what each value meant.
2. State the relevant mathematical vocabulary words you used to demonstrate your understanding. In every explanation, I tried my best to use mathematical vocabulary. For example, when I was talking about the “a” value I talked about how it stretched or compressed. I also talked about how it reflected. I also stated several times words like parent function, parabola, shifted, and more throughout the other explanations.
3. How did you use formatting to share this information in a clear and organized way? The way I formatted my desmos graph by having both parabolas in one photo makes it easier and clearer to see. Me explaining what the colour of the parabola represents, makes it easier for the person to understand, which function is which in the photo. The captions for the equations also make it easier to understand which parabola is the parent function and my own function.