Math 2Name______

Lesson 3-2:Designing Parabolas, Part 1

Learning Goals:

  • I can identify which parts of the function indicate, if applicable, the function’s y-intercept, x-intercept(s), increasing intervals, decreasing intervals, minimums, maximums, symmetries, end behaviors.
  • I can apply the zero product property to find the zeros of a quadratic function written in factored form.
  • I can write the equation that describes a quadratic function in factored form when I am given a graph with the x-intercept(s) and another point on the graph.

Recall from last unit, the coefficient of the x2 term, tells us a great deal about the parabola.

If f(x) = a · x2, then answer the following questions:

If a is positive, then which way does the parabola open? ______

If a is negative, then which way does the parabola open? ______

If |a| >1, then is the parabola vertically stretched or compressed? ______

If 0 < |a| < 1, then is the parabola vertically stretched or compressed? ______

Next, you are going to find the equation of the parabola going through the path of “Math-O the Magnificent” by applying what you reviewed up above, plus a little bit more . . . . .

NOTES:

  1. Does the parabola have a maximum or a minimum? ______

Based on your answer, what is the sign of a? ______

  1. Compared to the parent function, f(x) = x2 (also pictured in the graph above), is Math-o’s path a stretch or compression? ______

Based on your answer, what are some possible values of a? ______

3. What are the x-intercepts of the parabola? ( , 0) and ( , 0)

Write a pair of linear factors that would yield those x-intercepts: ( x )( x )

4. Now use your answers to questions 1, 2,3 to create an equation for Matho’s path.

Enter your equation in the calculator to test it out.

Describe how well your parabola fits Math-o’s path:

What adjustment(s) to your equation are you going to make to get a better fit?

Keep adjusting your A-value until you get a good fit.

Write your final equation in factored form: f(x) = ______OVER

Write an equation for the parabola that fits the satellite dish in the picture below:

This time do not guess & check. Set up an equation and solve for a. Show your work below:

NOTES:

Practice: Find the equation of the parabola below. Show your work.

Math 2Name______

Lesson 3-2: Designing Parabolas, Part 2

Learning Goals:

  • I can identify which parts of the function indicate, if applicable, the function’s y-intercept, x-intercept(s), increasing intervals, decreasing intervals, minimums, maximums, symmetries, end behaviors.
  • I can apply the zero product property to find the zeros of a quadratic function written in factored form.
  • I can write the equation that describes a quadratic function in factored form when I am given a graph with the x-intercept(s) and another point on the graph.

1.

Example

1b.1c.

Work to find minimum and y-interceptWork to find minimum and y-intercept

1d.1e.

Work to find maximum and y-interceptWork to find minimum and y-intercept

2. Write equations for quadratic functions whose graphs have the following properties.

DO ALL WORK ON A SEPARATE SHEET OF PAPER!!

Math 2Name______

Lesson 3-2: Designing Parabolas, Part 1 Homework

1.Use your understanding of quadratic functions to sketch graphs of the following functions.

Only use your calculator to check your final answer!

1a.1b.

OVER 

2.Write an equation for a parabola with the below conditions

2a.x-intercepts at and opening downward

2b.only one x-intercept at and a y-intercept at

Math 2Name______

Lesson 3-2: Designing Parabolas, Part 2 Homework

1.

OVER 

2. Use the graph and mark specific examples to illustrate the statements in parts a – d. If possible, label the

coordinates of any points you draw.

3. Simplify. Leave no negative exponents in your answers.