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# MATH 1060 w/ Peng Zhao - Week 1 - 2 Lectures - Sec. 1.1 & 1.2 MATH 1060Q - 100

UCONN

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This 5 page Class Notes was uploaded by Ambrosee Piresson on Monday September 12, 2016. The Class Notes belongs to MATH 1060Q - 100 at University of Connecticut taught by Peng Zhao in Fall 2016. Since its upload, it has received 58 views. For similar materials see Precalculus in Math at University of Connecticut.

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Date Created: 09/12/16

UCONN - MATH1060Q - Peng Zhao - Week 1 - Notes Sec. 1.1 - Rectangular Coordinates (aka: xy coordinates, Cartesian coordinates) Pythagorean Theorem Formula : a + b = c 2 c a b Notes: So A + B = C A B C C Distance Formula Formula: d = (x1- x2) + (y1- y2) y d = distance A (1,3) 3 ? B (4,2) 2 1 x 0 1 2 3 4 d = (4 - 1) + (2 - 3)
2 d = 9 + 1 = 10 d = 10
distance from A to B = d Mid-point formula y Formula: M = (x +1x )2 (y1+ y 2 A (x1+ x2) , 2 2 M midpoint B (y1+ y2) x 1 2 3 midpoint = 1 + 3 = 2 2 Translating Points 1,7) A = (1,2) Move/shift A up 5 units: (1, 2 + 5) = (1,7) y 3 Shift left 3 units: (1 - 3, 2) = (-2, 2) 2 A (1,2) (-2,2) 1 0 1 2 3 4 Sec. 1.2 - Graphs of equations Graph the equation: y = x + 1 (2,3) x = 0 y = 1 x = 1 y = 2 x = 2 y = 3 x = -1 y = 0 : : x : : Graph of y = x + 1 How about y = x 2 ——-> Quadratic function x = 0, y = 0 x = 1, y = 1 x = 2, y = 4 x = -1, y = 1 x = -2, y = 4 : : : : x parabola Graph of y = x 2 Intercepts: y x-intercept: let y = 0, solve x y-intercepts: let x = 0, solve y y - intercept x x -intercepts no intercept Intercept Example: y = x + 3 Find Intercepts. x - intercept: let y = 0 0 = x + 3 0 = x + 3 x = 3 y - intercept: let x = 0 y = x + 3 = 3 y Symmetry of the graph of y = f(x) (0,3) The three types of symmetry are: (1,2) x 1. Symmetric with respect to the x-axis y (x, y); (x, -y) both on the graph (0,-3)(1,-2) 1 y = f(x) - replace y by -y and
we will have the same equation -1 1 Example: x + y = 1 —> Circle equation 2 2 x replace y by -y = x + (-y) = 1 = x + y = 1 -1 y 2. Symmetric with respect to the y-axis: Replace x by -x to get the same equation Example: y = x + 1 2 Replace x by -x: = y = (-x) + 1 x y = x + 1 -x x y 3. Symmetric with respect to the origin (x,y) Replace x by -x, y by -y to get the same equation 3 x Example: y = x x —> -x y —> -y y = x —> -y = (-x) = -x 3 same (-x,-y) y = x 3 equation 3 3 3 y = x is not symmetric about the x-axis because y —> -y : -y = x is not y = x

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