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

by: Ambrosee Piresson

58

0

5

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

Marketplace > University of Connecticut > Math > MATH 1060Q - 100 > MATH 1060 w Peng Zhao Week 1 2 Lectures Sec 1 1 1 2
Ambrosee Piresson
UCONN

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This is everything the Professor wrote on the screen during class if you didn't have a chance to copy it down. A lot of formulas and examples, etc.
COURSE
Precalculus
PROF.
Peng Zhao
TYPE
Class Notes
PAGES
5
WORDS
CONCEPTS
Math, Precalculus, Pythagorean theorem, distance, formula, Midpoint_formula, Translating_points, graphs_of_equations, x-intercept, y-intercepts, Symmetry_of_the_graph, Linear Equations
KARMA
25 ?

## Popular in Math

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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