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Warm Up

Learn how to graph and identify transformations for circles and other parent graphs. Solve equations, identify horizontal and vertical movements, stretch and compress functions, and flip graphs. Practice with warm-up exercises, homework questions, and a quiz.

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Warm Up

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  1. I can transform circles and other parent graphs Warm Up • Solve: • Solve: • Solve for y: • Identify the transformation for each function: • b)

  2. Warm Up Solve:

  3. Warm Up Solve:

  4. Warm Up Solve for y:

  5. Warm Up Identify the transformation for each function: • b)

  6. Homework Questions

  7. Notes – Transformations of Graphs For equations solved for y: • H is the horizontal movement and is opposite • K is the vertical movement • A is the stretch/compression • If the function is stretched • If the function is compressed • If a is negative, the function is flipped

  8. Graphing Functions Not Solved for y How can we graph on our calculator? What about ? Solve for y.

  9. Graphing Functions Not Solved for y Solve for y: ? Graph the functions on your calculator. Notice how this graph has shifted compared to .

  10. Sleeping Parabolas is the parent function for a sleeping parabola. Graph each of the sleeping parabolas below and note their transformations. Can you come up with a general equation for a sleeping parabola?

  11. Sleeping Parabolas Quick Check Identify the transformation: • 3 Left 7, Down 2 Right 1, Up 4 Right 6, Compression 1/4 Left 3, Up 5 Stretch 4/3

  12. Graphing Parent Functions

  13. Shifting Circles Identify the center and radius of each circle: Center , radius 15 Center , radius 18 Center , radius 10 Center , radius 12

  14. Writing Equations Write the equation of… • A square root that has been shifted right 5, down 3 and compressed by 1/3 • A cubic function that has been shifted left 7, up 9 and stretched by 2 • A parabola that has been shifted right 10 and flipped upside down • A circle with center and radius 7 • A sleeping parabola shifted up 1 and left 3

  15. QUIZ You may use your notes. When done, put your quiz in the INBOX Homework: Transformations of Sleeping Parabolas and Circles WS

  16. Shifting _________ How could we graph Solve for y: What kind of function is this? A circle

  17. Shifting Circles Working in your groups, graph the circles below. Notice what shifts and what changes. Can you come up with a general equation for a circle?

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