Equation

y=x2 is the parent function while 𝑦=−1/2(𝑥−3)2 −4 is my given function.

Graph

Each line is colour-matched to the equations above, the red line is 𝑦=−1/2(𝑥−3)2 −4, while the purple line is the parent function y=x2.

Significance of a, h, an k in “y=a(x-h)2+k”

• “a” in my function is -1/2, the significance of it in my function is that it determines the width of the function. Since there is no “a” in the parent function it assumes its 1, so that for every “y” it equals x times itself. The width of the parabola is affected by “a”, as if the number is bigger the parabola is narrower, and if it’s smaller (like a fraction) it becomes wider as “a” gets closer to 0, if “a” is a positive number it will open upward with a minimum value and if it’s a negative number it will open downward with a maximum value.
• “h” in my function is 3 (because the original equation being (x-h)), h determines where the vertex of the function is on the x axis, as shown in the graph above the red line being my function is shifted over to positive 3 on the x axis (x=3). The parent function is on x=0 because theres no “h”, so it assumes it’s 0 since no number is given.
• “k” in my function is -4 and the significance of this number is that it determines the vertex on the y axis, in my function the line is shifted y=-4 down alongside x=3 from “h” above. Similar to “h” if theres no number representing “k” it’s just assumed to be 0 therefore the parent function is laying on (0,0) because of this.

Self-Assessment

• Q – Give an example from this assignment where you represented the same mathematical idea in multiple ways.
• A – I explained how “h” and “k” are similar in their rules on how it affects the vertex on both the x and y axis respectively, I stated that they share the rules that if there’s no number representing them it’s assumed to be 0 given the parent function.
• Q – Give an example from this assignment where you used mathematical vocabulary to demonstrate your understanding.
• A – I used terms like “function”, “vertex”, and “axis” to demonstrate my math vocab and also explain in the case of vertex what it does, it moves the point of the line on the x and y axis.
• Q – Give an example from this assignment where you used formatting to share the information in a clear and organized way.
• A – I used tools given from the blog editor such as headers and image embedding. I also presented my information in chronological order in relation to the requirements on teams. Lastly I used bullet points to separate the “a”, “h”, and “k” significances from each other as well as giving context to the screenshots above.