y=1/2(x-7)^2-1 (Standard/Vertex Form)

a

The “a” value in any equation will significantly impact the way your parabola looks. It is the variable that dictates whether your parabola opens up or down. If the “a” value is negative, this means our parabola will be opening downwards, indicating that our vertex is the maximum point. The reverse occurs when our “a” value is positive; it will open upwards, meaning the vertex is the minimum point. In my equation, the “a” value is positive, making it open upwards. However, the “a” value’s significance does not end there, as it also dictates the width of our parabola. In the example above, because our “a” value is greater than 0 but less than 1, we know the parabola will be wider. If my “a” value were to be greater than 1, the parabola would be narrower. Analyzing the graph above, we can see that our “a” value differs significantly from our parent function, as our parabola is significantly wider than the parent function.

h

When identifying the vertex of a parabola, the (h) value is half of the entire process. Our (h) value is crucial as it is our x coordinate for the vertex and determines the horizontal shift and the axis of symmetry for our parabola. If (h) is positive, your parabola will shift right and If (h) is negative, it will shift to the left. In our original equation, our (h) value is 7, allowing us to infer that our parabola will shift right, and our vertex will be (7,y). This means our vertex has shifted right from our parent function by 7 units.

k

The second half of finding our vertex, equally as important as (h), is the (k) value. This is what gives us our y coordinate to our vertex. The (k) value dictates the vertical shift of our parabola and represents the minimum/maximum value. With the example above our (k) value is -2 giving us a y coordinate to our vertex. This means our vertex has shifted down from our parent function by 2 units. Giving us the vertex of (7,-2).

Self-Assessment

How did you represent the same mathematical idea in multiple ways in this assignment?

During this assignment, I successfully displayed the same concept in two ways. I was given an equation and was able to take the information provided and present it algebraically-(Vertex/Standard form) and visually through my graph.

State the relevant mathematical vocabulary words you used to demonstrate your understanding.

• Vertex
• Axis of Symmetry
• Vertical/Horizontal Shift
• Standard/Vertex Form
  My Mathematical vocabulary allowed me to express and go deeper in my learning and display my understanding of the concept to the reader.
  

How did you use formatting to share this information in a clear and organized way?

For my assignment, I chose to break my points into 3 major topics. The (a), (h), and (k) values, organizing my essay in this format allowed me to go more in-depth with my understanding, express the concept as a whole, how it applies to my parabola, and how it differs from my parent function. It made the information easy to consume and left the reader with a deeper understanding of not only the concepts but how they are applied when given an equation.