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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

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Section 1.1

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  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

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