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MA112 – 1.1 Introduction to Graphing – Part A Today: Announcements finish notes on R.1 quiz on intervals plotting and ordered pairs finding distance equations for circles intercepts and graphing Homework 1.1 assigned on MyMathlab both R.1 and 1.1 due Monday Quiz Monday on calculating midpoint. Plotting Points / Cartesian coordinates A point (x,y) on the coordinate plane. x: location on the horizontal (x) axis. y: location on the vertical (y) axis. Distance and Midpoint Formulas (x1,y1) and (x2,y2) Distance: ( x1 x 2) 2 ( y1 y 2) 2 1 1 Midpoint: x1 x 2 , y1 y 2 2 2 Example: Sketch and find distance, midpoint for (1,3) and (-4,2). distance = (1 4) 2 (3 2) 2 = (5) 2 (1) 2 = 25 1 = 26 1 1 3 5 1 1 , midpoint = 1 4, 3 2 = 3, 5 = 2 2 2 2 2 2 What is a circle? A circle is a set of points that are a fixed distance from a center point. Standard Form for a Circle x h 2 y k 2 r 2 will have center (h,k) radius r This equation comes from the distance formula: distance of (x,y) from center (h,k) = r = ( x h) 2 ( y k ) 2 square both sides to get equation for a circle) Example: Sketch circle with center (2,0) and radius 3. Write standard form of the equation. x 22 y 02 32 MA112 – 1.1 Introduction to Graphing – Part B Today: quiz on midpoint equations and ordered pairs intercepts graphing (group worksheet) begin 1.2: Naïve concept of function. Announcements Homework 1.1 – Part B and 1.2 – Part A assigned in MyMathlab, due Wednesday group worksheet due Wednesday Equation: equality of terms with variables (x and y) Graph: The graph of an equation (with variables x and y) consists of the set of points (x,y) that satisfy the equation. Exercise: find an ordered pair (x,y) that satisfies the equation y = x+7. (x,y) = (1, ?) (x,y) = (?, 1) Is (10,3) a solution to this equation? Simple Graphing (1) make a T-table of (x,y) values for some permitted values of x and sketch them (2) find the intercepts, usually the easiest to find x-intercepts: where the graph intersects the x axis (to find, solve equation when y=0) y-intercepts: where the graph intersects the x axis (to find, solve equation when x=0) x-intercept: (?,0) y-intercept:(0,?) (3) choose ‘easy’ points to fill in your T-table and graph the function (4) experience teaches you how to graph more quickly worksheet: 4 graphs to draw (line, parabola, circle, absolute value) Experience teaches you how to graph more quickly: Graphs have certain predictable shapes x and y appear in an equation with power 1 example: y = x+2 line x appears in an equation with power 2, y appears with power 1 example: y=x2 + 7 parabola x appears in an equation with power 2, y appears with power 2 circle there will always be new graphs you don’t have experience with power of y=1 power of y=2 power of x =1 line or parabola power of x =2 or parabola circle (closed) or hyperbola (open)