Graph A (red): Quadratic parent function 𝑓(𝑥)=𝑥²
Graph B (blue): Opens up and is wider 𝑓(𝑥)= (x-0)²-2
Graph C (green): Opens down and is more narrow 𝑓(𝑥)= -6(x+0)²
Graph D (black): Shifted up 𝑓(𝑥)= 4(x-5)²+3
Graph E (purple): Shifted down 𝑓(𝑥)= 4(x-0)²-6
Paragraph
In the formula y=a(x-h) ² +k, H represents horizontals shifts of the parabola. If the value of H increases, it will shift to the right, if it decreases, it will shift to the left. An example of this would be one of my equations; y=4(x-5) ² +3, the value of H is positive 5, meaning it shifts 5 units to the right. This goes the same for K but represents the vertical shift of the parabola instead. If the K value increases, the parabola shifts up, if it decreases, it will shift down. So, by using the same equation, y=4(x-5) ² +3, the K is 3, meaning it shifts up 3 units. Compared to this equation; y=4(x-0) ²-6, K is –6, therefore, it will shift 6 units downwards. Overall, by adjusting both “H” and “K” values we can change the positions of the vertex of the parabola. As for “A”, it will affect the narrowness of the parabola. Therefore, if A is greater than 1 it will become more narrow. If A is between 1 and –1, the parabola will become wider. A also changed which direction the parabola is facing, so when A is negative, for example, y=-6(x+0) ², which has a negative 6 A value, it will open downwards. While in y=4(x-5) ², which has a positive 4 A value, it will open upwards. This represents the minimum and maximum value of a parabola.
How did you represent the same mathematical idea in multiple ways in this assignment?
I represented multiple math ideas by giving examples of equations to demonstrate what the h, k, and a values which corresponds to my parabola in desmos. Therefore, I displayed how the values changed my graph visually.
State some of the relevant mathematical vocabulary words you used to demonstrate your understanding.
In my reflection, I effectively used mathematical vocabulary to explain the quadratic formula, y=a(x-h) ²+k, explaining each of the following of H, K and A values I used terms such as horizontals shift, vertical shift which is the vertex position. In addition using “width”, “opening upwards” and “downwards” to explain A.
How did you use formatting to share your information in a clear and organized way?
I used formatting in Desmos, by adjusting the graph’s properties first. When creating equations, I made it simplistic, by using repetitive numbers, like 0’s. I labeled vertexes and color-coordinated each graph to differentiate them clearly to maintain organization. This approach helped me present the information effectively.
