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# Quadratics.

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### Quadratics.

1. 1. Graphing QuadraticswithMs. Schwartzpssstt…press the speaker!Graphing Quadratics
2. 2. Graphing QuadraticsThings you should know already…• What a quadratic is.• What a quadratic is.• What the vertex is.Just a heads up, you should be taking notes on graphpaper, I mean, you already knew that it is called“Graphing Quadratics.”
3. 3. Graphing QuadraticsThings you should know by theend…• How to graph a quadratic fromall three forms.• The three basic forms of theequation of a quadratic.
4. 4. Graphing QuadraticsKnow what you want? Go for it!VertexFormGraphingIdentifying FormsStandardFormZeroes FormAlready been through the lessons?Practice one of the followingDon’t know where to start?It’s cool, just click here.HINT: Use the left/rightarrows to navigate throughthe lessons or the menu barat the bottom to switchbetween themHINT: This button will alwaysbring you back to this slideBonus Material!
5. 5. Graphing QuadraticsVertex FormThe BasicsSo here the vertex isIt’s important to notice thatthe signs switch that isbecause the originalequation has minus signs infront of h and k.So here the vertex isYou should also notice thatthe a out in front does noteffect the vertex.Vertex StandardZeroes FormGo to….
6. 6. Vertex FormLet’s PracticeIdentify the Vertex Press over arrow to revealGraphing QuadraticsStandardZeroes FormGo to….Vertex
7. 7. Vertex FormCreating an x-y tableOnce you know your vertex you are going to want tocreate an x-y table.x y-101 623Put your vertex in the middlethen fill in your x column bygoing two numbers in eachdirection.Graphing QuadraticsStandardZeroes FormGo to….Vertex
8. 8. Creating an x-y tableOnce you know your vertex you are going to want tocreate an x-y table.x y-3 -10-2 -7-1 -60 -71 -10Fill in your y-values byplugging in for x.For example:Graphing QuadraticsStandardZeroes FormGo to….Vertex
9. 9. Graphing from an x-y tableNow you have 5 points. Graph them!x y-3 -10-2 -7-1 -60 -71 -10Graphing QuadraticsStandardZeroes FormGo to….Vertex
10. 10. Bam!You’re done.Your can now graph from vertex form.Well, maybe you should try one more.Try it first. The answer is on the next page.Graphing QuadraticsVertex StandardZeroes FormGo to….
11. 11. x y1 102 43 24 45 10Vertex Practice!Graphing QuadraticsVertex StandardZeroes FormGo to….
12. 12. Zeroes FormThe BasicsSo here the zeroes areIt’s important to notice thatthe signs switch becauseyou are setting x – 3 = 0and solving for x to find thezeros.So here the zeroes areYou should also notice thatthe a out in front does noteffect the zeroes.Graphing QuadraticsVertex StandardZeroes FormGo to….
13. 13. Zeroes FormLet’s PracticeIdentify the Zeroes Press over arrow to revealGraphing QuadraticsStandardZeroes FormGo to….Vertex
14. 14. Zeroes FormLet’s PracticeGraphing QuadraticsStandardZeroes FormGo to….Because a parabola issymmetric the x- coordinate ofthe vertex is exactly halfwaybetween the x-coordinates ofthe two zeroes . So, you wantto find the average of the twozeroes.To find the y-coordinate youplug the xv in to the originalequation and solve for yv.So the vertex is (1, 36).Vertex
15. 15. Creating an x-y tableOnce you know your vertex you are going to want tocreate an x-y table.x y-5 00 -351 -362 -357 0Fill in your y-values byplugging in for x.For example:Graphing QuadraticsStandardZeroes FormGo to….HINT: Use your zeroes inyour x-y table. Its like gettingtwo free points!Vertex
16. 16. Graphing from an x-y tableNow you have 5 points. Graph them!Graphing QuadraticsStandardZeroes FormGo to….x y-5 00 -351 -362 -357 0Vertex
17. 17. Kazam!You’re done.Your can now graph from zeroes form.Well, maybe you should try one more.Try it first. The answer is on the next page.Graphing QuadraticsStandardZeroes FormGo to….Vertex
18. 18. x y-8 00 16-2 18-4 164 0Zeroes Practice!Graphing QuadraticsStandardZeroes FormGo to….Vertex
19. 19. Graphing QuadraticsStandardZeroes FormGo to….Standard FormThe BasicsSome ExamplesVertex
20. 20. Graphing QuadraticsStandardZeroes FormGo to….Standard FormFinding the vertexTo find the x coordinateof the vertex you will usethe equation:Vertex is:To find the y-coordinate you plug the xv in to theoriginal equation and solve for yv.Vertex
21. 21. Creating an x-y tableOnce you know your vertex you are going to want tocreate an x-y table.x y0 -61 32 63 34 -6Fill in your y-values byplugging in for x.For example:Graphing QuadraticsStandardZeroes FormGo to….HINT: Remember quadraticsare symmetric!Vertex
22. 22. Graphing from an x-y tableNow you have 5 points. Graph them!Graphing QuadraticsStandardZeroes FormGo to….x y0 -61 32 63 34 -6Vertex
23. 23. Yahoo!You’re done.Your can now graph from standard form.Well, maybe you should try one more.Try it first. The answer is on the next page.Graphing QuadraticsStandardZeroes FormGo to….Vertex
24. 24. x y-1 20 -101 -142 -103 2Standard Form Practice!Graphing QuadraticsStandardZeroes FormGo to….Vertex
25. 25. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.Identifying Forms PracticeEach slide will have 1 equation. Write down theequation and form you think it is then hit the overarrow to reveal the form.
26. 26. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.Vertex form
27. 27. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.Standard form
28. 28. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.Vertex form
29. 29. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.Vertex formBut move the 5 over and it’s standard.
30. 30. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.Zeroes Form
31. 31. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.Standard formNotice in this one b=0.
32. 32. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.Zeroes Form
33. 33. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.Standard formor Vertex Form
34. 34. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.Zeroes Form
35. 35. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.Nice Practice!Did you get them all?If not, take a minute and note downwhy you missed what you missed.Now, head back home and either practice graphing orreview another section!
36. 36. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.GraphingUnder the first hidden area will be the x-y table.Under the second will be the graph.Also, remember there is a link at the bottom if youneed to go back and review.
37. 37. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.x y-3 0-1.5 5.25-.5 -6.25.5 5.252 0Check yourx-y tableCheck yourgraph
38. 38. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.x y1 02 -63 -84 -65 0Check yourx-y tableCheck yourgraph
39. 39. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.x y0 1-1 13-2 17-3 13-4 1Check yourx-y tableCheck yourgraph
40. 40. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.x y-2 13-1 100 91 102 13Check yourx-y tableCheck yourgraph
41. 41. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.x y1 -60 3-1 6-2 3-3 -6Check yourx-y tableCheck yourgraph
42. 42. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.x y-2 13-1 100 91 102 13Check yourx-y tableCheck yourgraph
43. 43. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.x y1 4/32 1/33 04 1/35 4/3Check yourx-y tableCheck yourgraph
44. 44. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.Nice Job!Want some Bonus Materials?Graphing onyour calculator.Review withoutside sources!Finding thevertex on yourCalculator.
45. 45. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.Bonus MaterialsGraphing on your CalculatorClick on the video below to start
46. 46. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.Review with outside sources!This is an awesome videoshowing someone graphingone quadratic in each form.This is Purple Math’s pageon graphing quadratics.This is Khan Academy’sreview of graphing in allforms.(This one is interactive.)
47. 47. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.Bonus MaterialsFinding the Vertex on your calculatorClick on the video below to start
48. 48. Graphing QuadraticsVertex StandardZeroes FormIf you can’t remember or need a refresher head back to any of the sections.That’s it!If you’ve made through all the practice andall the units you are done!Thanks for being awesome!