GRAPH:
![](https://mycentennial.sd43.bc.ca/jordyny2021/files/2024/04/desmos-graph-fa22a1d84ff0a1aa-1024x1024.png)
Graph A (RED): Quadratic parent function f(x) = x^2
Graph B (BLUE): Opens up and is wider than the parent function f(x) = 1/5x^2
Graph C (GREEN): Opens down and is narrower than the parent function f(x) = -4x^2 + 5
Graph D (ORANGE): Parabola that is shifted to the right of the parent function f(x) = 2/5(x-6)^2 + 2
Graph E (PURPLE): Parabola that is shifted lower than the parent function f(x) = 1/2(x-6)^2 – 2
PARAGRAPH
In my equations, the variables a, h, and k change the width, the position of x, and the position of y. The example I will be using is f(x) = 2/5(x-6)^2 + 2, which is Graph D in this assignment. In this equation, +2/5 describes how wide the parabola will be and how the parabola will open up. In this equation since +2/5 is a positive fraction, the parabola will open upwards compared to another equation, like f(x) = -4x^2 + 5, where the a is a negative number. -6 is the h in this equation and it describes where the parabola will be placed horizontally on the graph. Since the equation is f(x) = a(x-h)^2 + k, the h being a negative means that the number we are using is positive, so the x on the vertex will be +6. The k is +2, and it describes where the parabola will be placed vertically on the graph. Since the k is a +2, the parabola will be shifted to the right 2 times. If the k was a negative, it would have been shifted left 2 times.
SELF-ASSESSMENT
I was able to show the main mathematical idea multiple times by using the same equation but changing the values each time. In the equation f(x) = a(x-h)^2 + k, changing each variable changes the position, width and direction that the parabola is going in. Being able to the use the same formula while changing the parabolas is useful to keep the same mathematical idea throughout the assignment. Some vocabulary I used while showing my understanding include vertex, parabola, positive, negative, horizontally, and vertically. I used the formatting to show and label each point on the graph using bold colors and words. I was also able to show the numbers on the graph going up from one so it looks organized. Lastly, I removed minor guidelines to make the graph look neater.