View Resource: Analyzing the effects of the changes in a on the graph of y = ax^2 +c

Resource ID: OT1621

Analyzing the effects of the changes in a on the graph of y = ax^2 +c

By: TEA

Series (3)

1. Analyzing the Effect When a > 1 [[176]]

  1. Click on the Interactive exercise. Assistance may be required. icon to access an online graphing calculator - Graphit

    Directions:

    You will be entering quadratic equations in the y(x) field. (Remember, this is function notation. It is just a different way of writing a "y =" equation.) To enter the exponent of the equation y(x) = x2; use the ^ symbol which is accessed by pressing "Shift 6". The equation will be written in the y(x) field as x ^ 2. At any time click on "Show Tabular Data" to see a table of values.

    1. Enter x2 in the y(x) field and then click on Plot/Update to graph the equation.
    2. Go to the next line in the y(x) field and enter 2x2. Then click on Plot/Update. A snapshot of your entries is shown.
    3. Go the next line in the y(x) field and enter 5x2. Then click on Plot/Update.
    4. On your own paper, describe how changing the coefficient of x from "1" to a number greater than 1 affects the graph. (Use the words narrower or wider.)

    Check Your Answer

    The larger the value of a  the narrower the graph of the function.

    Source: Analyzing the Effect When a > 1, Texas Education Agency / University of Texas at Austin
    Source:  Interactive Graphit, CSERD, A Pathway Portal of NSDL

2. Practice Exercise [[177]]

  1. On your own paper, describe how the graph of y = ax2 will be affected by each of the following changes. (Use the words, narrower, wider, and reflection). You may use a graphing calculator if necessary.

    1. The value of a is 8.

    Answer

    The graph (or parabola) will be narrower.
    2. The value of a is -1.

    Answer

    The graph (or parabola) will be reflected across the x-axis.
    3. The value of a is 2 7

    Answer

    The graph (or parabola) will be wider.
    4. The value of a is -  1 8 .

    Answer

    The graph (or parabola) will be reflected across the x-axis and will be wider.
    5. The value of a is -6.

    Answer

    The graph (or parabola) will be reflected across the x-axis and will be narrower.
    6. Which of the functions listed below has the narrowest graph?
    y = 7 3 x2, y = 3x2, y = 2 3 x2, y = 2x2

    Answer

    y = 3x2
    7. Which of the functions listed below has the widest graph?
    y = 7 3 x2, y = 3x2, y = 2 3 x2, y = 2x2

    Answer

    y = 2 3x2

    Source: Practice, Analyzing the effects of the changes in a on the graph of y = ax^2 +c, Texas Education Agency / University of Texas at Austin

3. Join the Course [[262]]

  1. OnTRACK Lessons for Algebra I are supplementary lessons that align with the Texas Essential Knowledge and Skills. The lessons use video, graphics, and online activities to support classroom instruction and facilitate individualized intervention for students. While these lessons are organized as a Project Share “course,” they do not cover every student expectation in the TEKS for the corresponding SBOE-approved course. Students cannot earn course credit by completing OnTRACK lessons.

     

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