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 = x2 + 2
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
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.
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
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
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
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
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.
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.
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)?
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