List of Equations

Red Parabola:

Blue Parabola:

Orange Parabola:

Purple Parabola:

Green Parabola:

Significance of a, h, and k in My Chosen Equations

In the graph that I’ve created, each parabola shows how changes to the values a, h, and k affect the parabola’s shape and position along the graph.

The a-value controls the parabola’s vertical stretch or compression and direction. When a-value is greater than 1, the parabola becomes narrower, meaning it is vertically stretched. If a is a fraction between 0 and 1, it means that the parabola widens. If the parabola is a negative number, it opens downwards instead of upward, flipping it vertically. For the green parabola, my a-value was 5 making it more narrow, whereas, the blue parabola’s a-value was a fraction, making it wider. The blue parabola’s a-value was also negative, making it open downwards, and the green parabola’s a-value was positive so it remained opening upwards.

The h-value of a parabola shifts it horizontally along the x-axis. Positive h-values move the vertex to the right, while negative h-values move it to the left. This horizontal movement changes the location of the parabola’s vertex and points, but it doesn’t affect the parabola’s shape or direction. The purple parabola had a h-value of 3, making it shift to the right by 3, which changes the parabola’s vertex and other points.

The k-value of the parabola shifts it vertically along the y-axis. Positive k-values move the parabola upwards, and negative k-values move it downwards. This change impacts the y-coordinate of the vertex, which changes the minimum or maximum value, depending on the direction the parabola opens. The orange parabola’s k-value was 2, making it shift upwards along the y-axis by 2. This changed the minimum value of the parabola and changed its location.

Self-Assessment

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

In this assignment, I represented the same mathematical idea of transforming parabolas in multiple ways. First, I used the graph on Desmos to show visual changes to the parabolas, which shows how adjusting the a,h, and k values affected each parabola’s shape and positioning along the graph. After that, I included the equations of each transformed parabola, which represented these transformations in an algebraic form. I think by combining the visual and symbolic representations, I demonstrated the impact of adjusting the a,h, and k values on parabolas in multiple ways.

State some of the relevant mathematical vocabulary words you used to demonstrate your understanding and their definitions. State where you found the definitions

All the definitions I have used in this Edublog have been words I have learned in class either from our lessons or from other students.

• Vertex: The vertex is the highest or lowest point of a parabola, depending on which direction it opens. For parabolas we have been learning, in form y = a(x-h)^2 + k, the vertex is located at the point (h,k). This point determines the position of the parabola on the graph.

• Transformation: A transformation is like an operation that changes the position, shape, or orientation of a graph. In this assignment, the transformations include shifting the graph horizontally, and vertically, and stretching or compressing it. Each transformation changes depending on which values are changed in the equation.

• Vertically Stretching or Compressing: This describes how the parabola’s width changes based on the value of a, in the equation. If the a-value is greater than 1 the parabola stretches vertically, if the a-value is less than one and larger than 0 (a fraction) the parabola becomes compressed, making it wider.

• Horizontal and Vertical Shifting: Horizontal shifts move the parabola left and right, controlled by the h-value. Vertical shifts move the parabola up and down, controlled by the k-value. These shifts adjust the position of the vertex and parabola without affecting its shape.

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

I used formatting to keep my information clear and organized in several different ways. First off, I used headings to separate each section, making it easy to find specific parts like the equations, paragraph explanation, and self-assessment. I also used bullet points to organize my definitions and make them clear and easy to understand. I used bold text to highlight key terms and my questions so they don’t blend in with the rest of my writing. This formatting made my post look clean and will help guide the reader through my assignment.