Tag Archives: #communicationcc

Quadratic Equations in Vertex Form

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  1. The solid red parabola represents the parent function, with no transformations applied, meaning the vertex is (0,0).
  2. The solid blue parabola has been transformed by the values a=1, h=0, and k=5. The coefficient a=1 means the parabola opens upwards and has not been stretched or compressed, while h=0 means that the parabola has not been shifted left or right, the axis of symmetry remains 0, and k=5 means it has a vertical shift upward of 5. The vertex of this parabola is (0,5).
  3. The solid green parabola has been transformed by the values a=1, h=0, and k=-6. The coefficient a=1 means the parabola opens upwards and has not been stretched or compressed, while h=0 means that the parabola has not been shifted left or right, the axis of symmetry remains 0, and k=-6 means it has a vertical shift down of 6. The vertex of this parabola is (0,-6).
  4. The solid purple parabola has been transformed by the values a=1, h=-7, and k=0. The coefficient a=1 means the parabola opens upwards and has not been stretched or compressed, while h=-7 means that the parabola has been shifted horizontally to the left, the axis of symmetry is -7, and k=0 means the parabola has no vertical shift. The vertex of this parabola is (-7,0).
  5. The solid black parabola has been transformed by the values a=1, h=7, and k=0. The coefficient a=1 means the parabola opens upwards and has not been stretched or compressed, while h=7 means that the parabola has been horizontally shifted to the right, the axis of symmetry is 7, and k=0 means the parabola has no vertical shift. The vertex of this parabola is (7,0).
  6. The dashed red parabola has been transformed by the values a=1/5, h=0, and k=-3. The coefficient a=1/5 means the parabola opens upwards and demonstrates a vertical compression, while h=0 means that the parabola has not been shifted left or right, the axis of symmetry remains 0, and k=-3 means that the parabola has been vertically shifted down by 3 units. The vertex of this parabola is (0,-3).
  7. The dashed green parabola has been transformed by the values a=5, h=12, and k=0. The coefficient a=5 means the parabola opens upwards and has been vertically stretched, while h=12 means that the parabola has been horizontally shifted to the right, the axis of symmetry is 12, and k=0 means that the parabola has no vertical shift. The vertex of this parabola is (12,0).
  8. The dashed black parabola has been transformed by the values a=-5, h=12, and k=0. The coefficient a=-5 means the parabola opens downwards and has been vertically stretched, while h=12 means that the parabola has been horizontally shifted to the right, the axis of symmetry is 12, and k=0 means that the parabola has no vertical shift. The vertex of this parabola is (12,0).

Communication Core Competency Reflection:

In this assignment, I demonstrated that I can understand and share information in a clear, organized way by individually describing how each parabola’s shape and position were transformed by the values of a, h, and k. I explained how each value affected the parabolas while considering what I was going to convey and to whom I was going to convey it to. Using appropriate mathematical vocabulary and presenting my explanations in a logical order allows my teacher and peers to clearly understand and follow the information I am communicating. This assignment allowed me to strengthen my ability to understand and communicate mathematical concepts through writing.

Domain & Range

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State the domain and range of your graph using proper notation.

Domain: x ∈ R Range: y ∈ R

Explain what the domain and range mean in words

Domain refers to all the possible input values we can plug into a function. Domain refers to the x values on a graph.

Range refers to all the possible output values of a function. Range refers to the y values on a graph.

Is your graph a function or not? Explain how you can tell

My graph is a one-to-one function. Using the vertical line test you can confirm that the graph is a function by checking that the vertical line only touches the graph at one point at a time. Using the horizontal line test you can confirm that the graph is a one-to-one function by checking that the horizontal line only touches one point of the graph at a time.

Self-Assessment

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

In this assignment, I represented the same mathematical equation as both a graph and an equation. The graph provides a visual representation of the equation, making it easier to understand, unlike the equation, which may be harder to interpret.

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

In this assignment, I used mathematical vocabulary such as domain, range, function, and one-to-one function to describe and analyze my graph. These terms helped me clearly explain the details of my graph and demonstrate my understanding.

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

In this assignment, I used headings and bold text to organize my responses and clearly separate my work into different sections. This made the information easier to understand and follow. For example, I used the heading Self-Assessment to show where the topic shifted to a new idea, helping the reader understand the new focus of the section.