Category Archives: Math 11

Transforming Parabolas

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Parent Function: y=x^2

My Equation: y=1/2(x-7)^2-1

Significance of a, h and k:

“a” which is 1/2 in my equation is significant because it makes the parabola above stretch horizontally. Generally when “a” is positive like my “a” in my function above, the parabola opens upwards. Although if “a” was negative the parabola would open downwards. Another factor that would play a pivotal role to the shape of the parabola is the value when “a” > 1 and “a” <-1, the parabola compresses horizontally. On the other-hand, when “a” is 0<“a”<1 and -1<“a”<0 the parabola stretches horizontally.

“h” which is the horizontal shift of the x value of the vertex. So in my equation specifically inside the brackets is (x-7) which means the original x value was positive 7 in the x value of the vertex. Causing the parabola to horizontally shift 7 to the right. Essentially your “h” determines the value of x where your vertex opens up.

“k” which is -1 in my equation, is my constant and vertical displacement which shifts the parabola down 1. The value of “k” is the y-coordinate of the vertex of the parabola. In this equation, k=-1 which means the vertex of the parabola is at y=-1.

Overall, the equation y=1/2(x-7)^2-1 represents a parabola that opens upwards, has a vertex of (7, -1) which shifts the parabola 7 times to the right and down once while the parabola compresses horizontally.

Core Competency – Communication

1) Give an example from this assignment where you represented the same mathematical idea in multiple ways?

An example would be when explaining the significance of “h” and “k”, they were both determined from the vertex. The idea that both played a crucial role to the displacement of the parabola in terms of where it’s located on the graph.

2) Give an example from this assignment where you used mathematical vocabulary to demonstrate your understanding.

The value “a” determines the shape of the parabola, while the coordinates of the vertex, “h” and “k”, determine its position.

3) Give an example from this assignment where you used formatting to share the information in a clear and organized way.

I used headings in bold, dark letters to organize sections to allow the readers to follow along clearer with titles to describe each section.

Facing a Challenge

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Problem:


At first glance, this equation appeared to be very complex, and I was unsure of how to approach it. However, after reviewing the material and practicing more problems, I was able to overcome this challenge.

The first time I attempted this problem, I found it challenging because I did not have a clear understanding of how to solve radical equations. I was confused by the square roots on both sides of the equation and was unsure of how to isolate the variable. I felt overwhelmed and unsure of how to proceed.

The mistake that I made the first time I attempted this problem was that I did not correctly apply the rules of algebra to isolate the variable. Specifically, I was unsure of how to eliminate the square roots on both sides of the equation. I mistakenly squared both sides of the equation to get rid of the square roots, but I did not realize that this would be an extraneous solution. This led to an incorrect answer and caused me to become more confused and frustrated. But through reviewing the material and practicing more problems, I was able to gain a better understanding of the concept and solved the question. I now feel more confident in my ability to solve radical equations.