3.3: Quadratic Functions & Their Properties
f(x) = ax2 + bx+ c
a, b, and c are real numbers; a at 0; Domain: (oo, 00)
When graphed, quadratics result in a PARABOLA!

_
The vertical line passing through the vertex is called the axis of symmetg.
Equation
1.2: Intercepts, Symmetry, & Graphing Equations
Finding Intercepts
' Find xintercepts by letting y = 0
Find yintercepts by letting x = 0
Ex #1: Find the xintercepts and yintercepts for y = x2 . 1.
X~ln+eufei+j (3 :o) I E, fjllWEjfl (no)
Ozxt'l 3:3
3.2: Linear Models (Scatter Plots)
Ex #1. (a)
a) Use a graphing utility to draw the scatter plot.
b) Determine whether the graphed data appears
to follow a linear pattern.
c) If the data appears linear, use a graphing utility
to find the line of best fit
1.2: (Day 2) More Symmetry & Graphing!
Test for Symmetry in an Equation
xaxis symmetry: replace y with y and check for equivalent equation
yaxis symmetry: replace x with x and check for equivalent equation
origin symmetry: replace BOTH x and y with x and
6.5: Graphs of Tangent and Cotangent
Z = tanx
domain: All real numbers, EXCEPT add 71
2
range: (oo, 00)
period: 7r
xintercepts: at whole values ofn
yintercepts: (0,0)
oddrc
2
vertical asym ptotes: at
In order to graph a full period ofy = tanx
3.1: Linear Functions & Their Properties
f(x) = mx + b
m = slope; b = yintercept; Domain: (oo, 00)
Average Rate of Change: 2: = m
Ex #1:f(x) = 2x + 3 O3 34
a) slope? yintercept? III. I.
IIIIII IUIIIII
IIIII IIIIII
IIIII "IIIII
IIIII IIIIII
III
3.4: Building Quadratic Models
Ex #1: The price (p) in dollars and the quantity (x) sold of a certain product obey the demand equation:
p = %x + 100.
a) Find a model that expresses revenue (R) as a function of x. (R = xp)
b) Find the domain of R.
c) What
3.3: (Day 2) Vertex Form of a Quadratic
Ex #1: Determine whether the given quadratic function has a maximum value or minimum value. Then, find
the Value. 0,: 2 b, 1 c, O 5 a > O QM
_ _ = 2 _ o) 50 p ape
f(x) 2x + 12x 3 :>M4\Acmuw\ VAQUQ, @vui'ex
: ._LZ
7.1: Inverse Sine, Cosine, and Tangent
Inverse Sine
Inverse answers for sine will only be angles in: (QI 8: 5212
Positive: Q1;
Negative: Q g
Inverse Cosine
Inverse answers for cosine will only be angles in: Q1: & Q1:
Positive: (3:
Negative: QE
Inverse
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