View Resource: Analyzing the Effect of the Changes in c on the graph of y = ax^2 +c

Resource ID: OT1631

Analyzing the Effect of the Changes in c on the graph of y = ax^2 +c

By: TEA

Series (3)

1. Exploring the effects on y = ax + c when c > 0 [[181]]

  1. In this part of the lesson, you will be investigating how changing the value of c to a number greater than 0 will affect the graph of y = ax2 + c

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

    Directions for the Graphing Calculator:

    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 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.


    Source: Graphit, Shodor

    1. Enter x2 in the y(x) field and then click on Plot/Update to graph the equation.
    2. Click "Enter" to go to the next line in the y(x) field and enter x2 + 1. Then click on Plot/Update.
      A snapshot of your entries is shown.
    3. Click "Enter" again and enter x2 + 6. Then click on Plot/Update.

    Check Your Answer

    When the value of c is greater than 0, all points on the graph are shifted up c units.

    Source: Exploring the effects on y = ax + c when c > 0, Texas Education Agency / University of Texas at Austin
    Source: Interactive Graphit, CSERD, A Pathway Portal of NSDL

2. Exploring how Changes in c Effect the Equation of a Parabola [[182]]

  1. Let's look at how the equations of y = x2 + c move the parabola.

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

    At any time you may click on "Show Tabular Data" to see a table of values.

    1. Enter x2 + 3 in the y(x) field and then click on Plot/Update to graph the equation.
    2. Go the next line in the y(x) field and enter x2 – 1. Then click on Plot/Update.
    3. How many units down did the parabola move? Check Your Answer

      4 units.
    4. Shift the equation y = x2 – 3 up 7 units, what is the new equation? Check Your Answer

      y = x2 + 4 because -3 + 7 = +4

    Source: Exploring how Changes in c Effect the Equation of a Parabola, Texas Education Agency / University of Texas at Austin
    Source: Interactive Graphit, CSERD, A Pathway Portal of NSDL

3. Join the Course [[260]]

  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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