1 / 36

Section 1.1

Section 1.1. Graphs of Equations. What you should learn. How to sketch graphs of equations How to find x- and y-intercepts of graphs of equations How to use symmetry to sketch graphs of equations How to find equations and sketch graphs of circles

cullen-short
Download Presentation

Section 1.1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 1.1 Graphs of Equations

  2. What you should learn • How to sketch graphs of equations • How to find x- and y-intercepts of graphs of equations • How to use symmetry to sketch graphs of equations • How to find equations and sketch graphs of circles • How to use graphs of equations in solving real-life problems

  3. Rectangular Coordinate System Origin y-axis Quadrants II I x-axis IV III Cartesian Plane

  4. Graph y = -2x + 1 • (0,1) • ( -1, 3) • ( 1, -1)

  5. Example A Sketch the Graph of an Equation

  6. Calculator • [y = ] • Enter y = 5 – 2x • [GRAPH] • [2ND] [TABLE] • Can you get this onto a piece of paper?

  7. Example B Sketch the Graph of an Equation

  8. Calculator • [y = ] • Enter y = x^2 – 5 • [GRAPH] • [2ND] [TABLE] • Can you get this onto a piece of paper?

  9. Intercepts of a Graph What can you tell me about intercepts?

  10. Intercepts of a Graph What can you tell me about intercepts?

  11. What can you tell me about intercepts? Intercepts of a Graph

  12. Intercepts of a Graph What can you tell me about intercepts?

  13. (0, y) (x, 0) Finding Intercepts • To find x-intercepts, let y be zero and solve the equation for x. • To find y-intercepts, let x be zero and solve the equation for y.

  14. Example C: Find the x- and y-intercepts of : (x, 0) (0, y)

  15. Example D: Find the x- and y-intercepts of : (x, 0) (0, y)

  16. Calculator • [y = ] • Enter y = (x+4)^.5 • Or y = √(x+4) • [GRAPH] • [2ND] [TABLE] • Can you get this onto a piece of paper? (x, 0) (0, y)

  17. Example E: Find the x- and y-intercepts of : (x, 0) (0, y)

  18. Calculator • [y = ] • Enter y = abs(2x+5) • To get “abs” • [math] Select NUM select [1 abs] • [GRAPH] • [2ND] [TABLE] • Can you get this onto a piece of paper?

  19. Example F: Find the x- and y-intercepts of : (x, 0) (0, y)

  20. Calculator • [y = ] • Enter y = 2x^3– 4x^2 –6x • [GRAPH] • [2ND] [TABLE] • Can you get this onto a piece of paper?

  21. 3 Flavors of Symmetry • X – Axis Symmetry • Fold the x-axis • (x, y)  (x, -y) • Y – Axis Symmetry • Fold the y-axis • (x, y)  (-x, y) • Origin Symmetry • Spin • (x, y)  (-x, -y)

  22. Example B X – Axis SymmetryFold the x-axis (x, y)  (x, -y)

  23. Example B Y – Axis SymmetryFold the y-axis (x, y)  (-x, y)

  24. Algebraic Tests for Symmetry • The graph of an equation is symmetric to the x-axis if replacing y with –y yields an equivalent equation. Since this is the equation we started with we know that the relation has x-axis symmetry.

  25. Algebraic Tests for Symmetry • The graph of an equation is symmetric to the y-axis if replacing x with –x yields an equivalent equation. Since this equation is different than what we started with we know that the relation does not have y-axis symmetry.

  26. They are symmetrical to each other but not to themselves.

  27. #29 y-axis symmetry

  28. #30 x-axis symmetry

  29. #31. Origin Symmetry

  30. 32. Y-axis symmetry

  31. a b Given:-Square-Length a a c c b Are the triangles congruent? c b c a What type of quadrilateral is formed by connecting the points? b a What is the area of the large square? What is the area of the small square? What is the area of all four triangles? = +

  32. a b Pythagorean Theorem (a+b)2 a c2 c c b c b c a b a What is the area of the large square? What is the area of the small square? What is the area of all four triangles? = +

  33. Distance Formula

  34. Circle • What is the radius? • What is a circle?

  35. Standard form of the Equation of a Circle

  36. Homework 1-31 odd, 57-71 odd 76

More Related