SWBAT… investigate transformations of quadratic functions. Tues, 5/8

Agenda 1. WU (5 min)2. Roots conclusions (5 min)3. TI-83 Graphing calculator investigation activity (30 min)

Warm-Up: 1.Take out hw#2: Compare your

answers with the posters in the back

HW#3

SWBAT… investigate transformations of quadratic functions. Tues, 5/8

Agenda 1. WU (5 min)2. Roots conclusions (5 min)3. TI-83 Graphing calculator investigation activity (30 min)

Warm-Up: 1. Take out hw#2 2. In baseball, a pop fly should be easily caught if it

stays in the air for 7 seconds. Suppose a ball that is hit can be represented by the function y = –16t2 + 125t + 5, where y is the height after t seconds. Will the ball be considered an easy catch? (Hint: use the graphing calculator)

HW#3

3 Types of Solutions1. Two real roots

1. Parabolas crosses two different points on the x-axis

2. Double root1. Parabola crosses the same point on the x-axis

3. No real roots1. Parabola does not cross the x-axis

Graphing Calculator Activity: Transformations

1. Each pair will be given a TI-83

2. You will be answering the questions on your worksheet that deal with the transformations of quadratics

3. You will be investigating three types of transformations

1. Vertical Translations

2. Dilations

3. Reflections

4. You have the class period today to finish this!

5. HW#3: Due tomorrow

SWBAT… use the Quadratic Formula to solve quadratic equations. Wed, 5/22

Today’s Agenda:

1. Finish your graphing calculator activity from yesterday (10 min)

2. Work on HW#3 (10 min)

3. Review HW#3 (10 min)

4

5. Lesson on Quadratic Formula (10 min)

Quiz tomorrow!!!

Transformations ConclusionsVertical Translation: The constant is where the parabola will cross the y-axis.

For example, y = x2 – 8 crosses the y-axis at -8

Dilation: The higher the value of a, the narrower the parabola

For example, y = 6x2 is narrower than y = x2

The smaller the value of a, the wider the parabola For example, y = 1/2x2 is wider than y = x2

Reflection: If a is negative the parabola is reflected across the x-axis.

For example, y = -x2 + 2 is reflected across the x-axis (upside down u)

Dave graphs the functions y = x2 and y = 1/4x2 + 2 on the same set of coordinate axes.

State two ways the graphs are different. Explain the reason for each difference.

Sample Correct Response

The graph of y = 1/4x2 + 2 will be wider than the graph of y = x2 because the coefficient of 1/4x2 is smaller.

The graph of y = 1/4x2 + 2 is two units higher because the y-intercept is (0, 2)

Scoring Guidelines2: The response provides two ways the graphs are different, along with an

adequate explanation of each difference.1: The response provides evidence of understanding.

For example, the response may: Include only one correct way the graphs are different, with an adequate

explanation. Include two ways the graphs are different, with little or no explanation.

0: Response is incorrect or irrelevant.For example, the response may: Include only incorrect ways the graphs are different, with no explanation. Restate the information provided in the item. Give irrelevant information.

Allison graphs the functions y = 4x2 and y = x2 – 3 on the same set of coordinate axes.

State two ways the graphs are different. Explain the reason for each difference.

Sample Correct ResponseThe graph of y = 4x2 will be narrower than the graph of

y = x2 – 3 because the coefficient of 4x2 is larger.The graph of y = x2 – 3 is lower because the -3 shifts

the graph down 3 units.

Scoring Guidelines2: The response provides two ways the graphs are different, along with an

adequate explanation of each difference.1: The response provides evidence of understanding.

For example, the response may: Include only one correct way the graphs are different, with an adequate

explanation. Include two ways the graphs are different, with little or no explanation.

0: Response is incorrect or irrelevant.For example, the response may: Include only incorrect ways the graphs are different, with no

explanation. Restate the information provided in the item. Give irrelevant information.

Find the domain and range of y = x2 + 5x + 6

Domain: All real numbers

To find the range, you need the vertex!

(-2.5, -0.25)

Range: y ≥ -0.25

Find the domain and range of y = x – 4

Domain: All real numbersRange: All real numbers

If f(x) = x2 – 6 and g(x) = 2x – 3, find f(g(x))