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Unit 1B quadratics

Reviewing how to graph quadratics, find vertex, axis of symmetry, maximum or minimum, and y-intercepts. Learn to identify intervals of increase and decrease for parabolas.

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Unit 1B quadratics

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  1. Unit 1Bquadratics Day 4

  2. Graphing a Quadratic Function EQ: How do we graph a quadratic function and identify all of its characteristics? M2 Unit 1B: Day 4 Lesson 3.1B

  3. Today, we are going to begin by reviewing what we have learned about graphing quadratics so far Lets recall how to find the following: • Vertex • AOS • Maximum or Minimum • Y-intercept

  4. Find: a) vertex b) axis of symmetry c) state whether the vertex is a maximum or minimum. d) y - intercept b = 4 a = -2, c = -2 a) Vertex: (1, 0) b) Axis of symmetry: x = 1 c) Since a < 0 , the parabola opens down and has a: maximum d) y-intercept: (0, -2) 4

  5. Find: a) vertex b)axis of symmetry c) state whether the vertex is a maximum or minimum. d) y-intercept b = 0 a = 1, c = 2 a) Vertex: (0, 2) b) Axis of symmetry: x = 0 c) Since a > 0 , the parabola opens up and has a: minimum d) y-intercept: (0, 2) 5

  6. Find: a) vertex b) axis of symmetry c) state whether the graph has a maximum or minimum. d) y - intercept a = -3 h = 1 k = 2 a) Vertex: (1, 2) b) Axis of symmetry: x = 1 c) Since a < 0 , the parabola opens down and has a: maximum d) y-intercept: (0, -1) 6

  7. Domain VS. Range • Domain: (x – values) read domain from left to right • Range: (y-values) read range from bottom to top

  8. Yesterday we said that the DOMAIN of parabolas is all real numbers…unless the parabola looks like this and has endpoint(s) We say the domain is restricted, therefore it is no longer all real numbers 8

  9. Find the domain of the graph below Domain: -1 < x < 2 9

  10. Find the domain of the graph below Domain: -2 < x < 2 10

  11. Find the domain of the graph below Domain: 11

  12. Graph the quadratic using the axis of symmetry and vertex. Axis of symmetry: Vertex: Y-intercept: One more point: Max or Min? maximum Extrema: y = 3 Domain: Range: All real numbers y ≤ 3 12

  13. Graph the quadratic using the axis of symmetry and vertex. Vertex: (-1, 0) Axis of symmetry: Y-intercept: One more point: Max or Min? minimum Extrema: y = 0 Domain: Range: All real numbers y ≥ 0 13

  14. Graph the quadratic using the axis of symmetry and vertex. Axis of symmetry: Vertex: Y-intercept: One more point: Max or Min? maximum Domain: Range: All real numbers Extrema: y = 5/4 14

  15. Stretch VS. ShrinkCompare the following graphs and equations: What is the difference between these two graphs when compared to the parent function? Vertical stretch Vertical shrink *note: rubber band

  16. Look at a couple more… What we should notice and confirm at this point is that the value of “a” determines how wide or narrow the graph will be… When ‌ a ‌ is greater than 1, we call that a vertical stretch When ‌ a ‌ is less than 1, we call that a vertical shrink

  17. State whether the graph shows a vertical stretch or vertical shrink Shrink…so |a| < 1 Stretch…so |a| > 1 Stretch…so |a| > 1

  18. Intervals of increase and decrease To determine the intervals of increase and decrease, you must “read” the graph from left to right What are these lines doing from left to right? 18

  19. Let’s apply this idea to parabolas… To determine the intervals of increase and decrease, you must “read” the graph from LEFT to RIGHT What is this parabola doing on the left side of the vertex? What is this parabola doing on the right side of the vertex? Going downhill Going uphill Interval of decrease Interval of increase 19

  20. One more… What is this parabola doing on the left side of the vertex? What is this parabola doing on the right side of the vertex? Going uphill Going downhill Interval of decrease Interval of increase 20

  21. Graph each quadratic function and determine the interval of increase and decrease Interval of decrease Interval of increase 21

  22. Graph each quadratic function and determine the interval of increase and decrease Interval of decrease Interval of increase 22

  23. Graph each quadratic function and determine the interval of increase and decrease Interval of decrease Interval of increase 23

  24. Determine if the given interval is an interval of increase or decrease decrease increase 24

  25. Determine if the given interval is an interval of increase or decrease increase increase 25

  26. Assignment: Day 4 Handout 26

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