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1.1 Graph of Equations

1.1 Graph of Equations. How to sketch graphs Find the intercept of a graph Use Symmetry to make graphs . Equations in 2 variables . 1 st degree equations are linear equations for example y = 4x – 6 2 nd degree equations are Quadratic equations for example y = x 2 + 2 . Linear equations.

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1.1 Graph of Equations

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  1. 1.1 Graph of Equations How to sketch graphs Find the intercept of a graph Use Symmetry to make graphs

  2. Equations in 2 variables • 1 st degree equations are linear equations for example y = 4x – 6 • 2 nd degree equations are Quadratic equations for example y = x2 + 2

  3. Linear equations • Have solutions of order pairs (x, y) x is part of the domain (input) y is part of the range (output) When x = 0, you have the y intercept When y = 0, you have the x intercept

  4. Quadratic equation • Graph a Parabola which have • A vertex, a focus and a directrix • Also, an Axis of Symmetry Symmetry is ability to fold the graph on itself across a point or line.

  5. There are 3 types of Symmetry Symmetric with respect to the x Axis Here (x, y) and (x, -y) are on the same graph Symmetric with respect to the y Axis Here (x, y) and (-x, y) are on the same graph Symmetric with respect to the origin Here (x, y) and (-x,-y) are on the same graph

  6. Symmetric with respect to the x AxisHere (x, y) and (x, -y) are on the same graph

  7. Symmetric with respect to the y AxisHere (x, y) and (-x, y) are on the same graph

  8. Symmetric with respect to the originHere (x, y) and (-x,-y) are on the same graph

  9. How to test for Symmetry Replace y with – y, if it does not change the equation it is symmetry “with respect to the x axis” x = 4y2 and x = 4(-y)2 are both the same

  10. How to test for Symmetry Replace x with – x, if it does not change the equation it is symmetry “with respect to the y axis” • y = 1/3x2 and y = 1/3(- x)2 are the same

  11. Symmetry for the origin Replace y with – y and x with - x, if it does not change the equation it is symmetry “with respect to the origin” x2 + y2 = 25 and (- x)2 + ( - y)2 = 25 are the same.

  12. How about y = | x – 2| is it Symmetric or not? • We could use a table • You could graph the equation to show • Or use an Symmetry Algebra tests of change x and y.

  13. The last thing in this Chapter is the equation of a Circle, you see this in Geometry and Algebra 2 • (x- h)2 + (g – k)2 = r2 • Do you remember what (h, k) where in the graph? • What does the r stand for in the equation? • How would you find the equation of a circle with a center at (2,3) and a point of (5, 7)?

  14. Homework • Page 9-11 #1-4, 5 , 8,12, 15, 24, 25, 28, 35, 42 47, 55, 60, 62, 73, 78, 84, 85, 88, 89

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