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Algebra II

Learn how to graph quadratic functions using transformations, such as translations, reflections, and stretches or compressions. Understand the key points on a parabola and how to determine the vertex. Practice graphing with tables and identifying characteristics of different quadratic functions.

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Algebra II

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  1. Algebra II Section 2.1 Using Transformations to Graph Quadratic Functions

  2. http://www.youtube.com/watch?v=ilhbOietyqA

  3. Recall the parent functions • Linear function f(x)= x • Quadratic function- f(x)=

  4. The quadratic function is a u-shaped curve called a parabola. • Five points are needed to graph a parabola- one at the turning point and two on each side.

  5. Graphing using a Table • The parent quadratic function has a turning point at (0,0). • State the translation for the above graph. • Where would the new “turning point” be? • Start your table of 5 points with the turning point

  6. Turning pt. Points to the right Points to the left

  7. We could also take the 5 points on the parent graph and move each point one place to the right and three up.

  8. Be attentive to signs when making a table for quadratic functions! • A negative squared is a positive! • Note the difference between (x)² and

  9. Graph a function with Each function is a quadratic Make a table- start with x=0 Make a table choosing some points to the right and some points to the left. You may need more than 5 if you don’t know the turning point. Plot the points and draw the parabola.

  10. Try these! Pg. 64 #2-4

  11. If the sign preceding the squared expression is positive, the parabola turns up. • If the sign preceding the squared expression is negative, the parabola turns down.

  12. Graphing parabolas using translations h moves the graph right when h h moves the graph left when h

  13. k moves the graph up when k k moves the graph down when k

  14. Each function is a quadratic Determine the translation to find the new “turning point” Move the 4 key points on the “parent” parobola the same way. Connect the 5 points and draw the parabola.

  15. The parabola in this form will have a vertex (turning point) at (h,k)

  16. Try these • Pg. 64 #5-7

  17. Vertex of a parabola- the lowest or highest point of a parabola

  18. When a number is placed outside the parentheses, it can result in a reflection across the x-axis, a stretch or a compression.

  19. The following letters represent constants. h- horizontal translation k-vertical translation a- reflection across the x-axis or a stretch/compression

  20. When is greater than 1, the parabola will be “skinny” • When is less than 1, the parabola will be “fat”

  21. For each parabola, state the vertex, describe it as “skinny” or “fat” and state whether it turns up or down. 1. 2. 3.

  22. 1. V(-6,-4), turns up, skinny 2. V(2,8), turns down, fat 3. V (-3,2), turns down, fat

  23. Try these! Pg. 64 #8-13 Don’t just move points if the graph has a stretch or shrink. Make a table starting with the vertex, with two points to the right of the vertex and two points to the left of the vertex.

  24. Classwork/homework Pg. 64 #17-25 odd, 26, 28, 39-41, 46-49

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