Red graph: The quadratic parent function y=đť‘Ą^2
Green graph: A parabola that opens up and is wider than the parent function y=1/5x^2 + 2
Black graph: A parabola that opens down and is more narrow than the parent function y=-4(x-2)^2 + 1
Blue graph: A parabola that has been shifted to the right of the parent function y=(x-3)^2 + 2
Purple graph: A parabola that has been shifted down lower than the parent function y=-1/8 (x+1)^2 – 1
Paragraph:
A, h and k were significant in my equations as they helped me achieve what was needed for each graph. In order to have a wider graph, I would have to change my a value to a fraction. The wider I wanted my graph, the smaller the fraction had to be. For example, if you look at my widest graph, the purple one, I have an a value of -1/8 (the negative determines that my graph is facing downwards). So then, if my a value was a greater number (that’s not a fraction), my graph would be narrow. You can see this in the black graph which has a a value of -4 (again, the negative only tells us that the graph opens downwards). The h value tells us how far left or right a graph is moved. We can see this in the blue graph, as it has moved 3 units along the x-axis. We can confirm this by checking its equation, where its h value is 3. Finally, the k value will determine how far up or down a graph has moved. The green graph has a k value of 2, so we can expect to see it translated 2 units along the y-axis.
How did you represent the same mathematical idea in multiple ways in this assignment?
I shown the significance of the a, h, and k values through the paragraph written above, and constructed translated graphs in Desmos. The equations I given for each graph have been listed below the image, which provides a clear translation from its parent function.
State some of the relevant mathematical vocabulary words you used to demonstrate your understanding.
Value. Fraction. Translation. Units. Axis. Negative. Equation.
How did you use formatting to share your information in a clear and organized way?
I followed and completed the instructions in order which arranged my Edu-blog, and I extended the clarity by italicizing a sentence/word that opens a new section. Also I took the advice of saving the image of the graph rather than editing on Edu-blog to avoid a blurry/messy image.