My parabola:

Standard parabola:

The Significance of a,h, and k

The ”a” variable in the formula to graph shifted parabolas determines how the width of a parabola or in other words, how wide a parabola will continue and open up throughout the graph. One thing to know about how determine if the parabola will be narrow or wide, if anything greater than 1 (y>1: 2, 3) for the a variable means it will be narrow.

The ”h” variable in the quadratic equation formula determines if the parabola you are trying to solve is going to be shifted on the right or the left side of the graph. Something to know and remember is that if you have a negative “h” variable, it will be on the positive side of the graph (the right side.) Then if you have a positive ”h” variable, it will be on the left side. Also, he ”h” variable determines where the axis of symmetry of your equation will be in the graph.

The ”k” variable in the formula, y=a(x-h)^2+k to solve shifted parabolas represents if the parabola that you are given is going to be shifted upwards or downwards. If your “k” variable is positive then your parabola is going to shift up and if k is negative, it will face down. The ”k” variable also determines the maximum or minimum value and what the y value of your vertex will be.

The Significance of a,h and k in my equation

For my a variable in my equation is -2. This means that in my parabola, it is narrow because if a is a number greater than 1, means the width of your parabola is going to be narrow.

For my h variable in my equation given, it is -6. H is where the location of your parabola is on the graph. Since ”h” is negative, my parabola is on the right side of the graph. Another thing to know is -6, my h value is what the axis of symmetry is.

For my k variable in my equation is +1. Because my k variable is a positive number, my parabola is shifted upwards because of this. Also, my parabola has a minimum value of 1 since the k variable represents what the minimum or maximum value will be.

Self Assessment

For me, I think I understand information when it is shown to me visually and is represented in pictures, graphs, etc. For this assignment, I tried to make this organized and hopefully something easy to read and understand. For my parabola, I put my equation given into Desmos for it to help me understand where my graph is located and looks like.
An example of where I used mathematical vocabulary to show my understanding was when I was explaining the significance a,h, and k in my equation. I tried to include vocabulary to make sense of these terms, words like minimum value, maximum value, positive number and axis of symmetry.
An example from this assignment where I used formatting to share the information in a clear and organized way is keeping the assignment well formatted and putting headings of each topic.

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Graphing a Parabola