By Adam Kershner and Fred Chung
Key points
•Slope Intercept
•Supply and demand
Linear function is F(x) = mx + B
M stands for the
slope. The slope is
the average rate of
change.
B is the Y
intercept
How to find the slope of a linear function
To find the slope of a linear
function you need to
calculate the change in Y
over the change in X. Or
using the formula:
Y2 – Y1
X2 – X1
The slope is increasing if
m is positive. The slope
is decreasing if m is
negative. The slope is
constant if the slope is
zero.
Y = 4X + 10
The slope in this problem is positive
Point Slope Form
y – y1 = m( x – x1)
Y - Cordinate
Slope
X - Cordinate
Recommended Problems for 3.1 are:
13, 18, 19,23, 24,
27, 32, 41, and 47
3.2
Building Linear
Functions from Data
•How to Graph
•Line of Best Fit
Scatter Plots
A scatter plot is linear
when the dots are close to
each other.
(X, Y)
Moves left and
right
Moves up
and down
A scatter plot is nonlinear
if the dots are more
spread out.
How to find Line of best fit
You can either
use a calculator
or do it by hand.
When you find the line
of best fit by hand you
find the slope between
two points that are on
opposite sides of the
points.
With a calculator
you use the
LINear
REGression
command.
Recommended Problems for
3.2 are:
3, 7, 9, 14, 21
3.3
Quadratic Functions
and Their Properties
•Shape of Parabola
•Graph by Steps
•Graph by Transformations
•Finding Mins and Max
Quadratic Functions
F(x) = ax2 + bx + c
A quadratic Function
is in the shape of a
parabola
If a is positive then it
opens up
If a is negative then it opens
down
Pg. 141
Graphing by Steps
When a gets bigger the graph becomes
narrower when it gets smaller the graph
becomes wider.
The X coordinate of the vertex is
found by using the formula:
-b
2a
To find the y intercept
put in 0 for x
To find the Y coordinate you
substitute the x value into the
function
To find the x coordinates use the
quadratic formula
Put all these parts
together on a graph
and connect the lines
Pg. 141
Graphing by Transformations
First you need to complete
the square forming a
function that looks like:
2(X + 2)2 - 3
Shifts 3 units down
Causes a
vertical
stretch
Shifts two units
left
Finding Min and Max
If a < 0 then the Max is
found by using:
-b
2a
If a > 0 then the Min is
found by using:
-b
2a
Recommended Problems for
3.3 are:
18, 21, 27, 44, 47, 57, 59, 64
3.4
Quadratic Models;
Building Quadratic
Functions from data
•Maximizing Revenue
•Analyzing the Motion of a Projectile
•Linear Regression on a calculator
Maximizing Revenue
Analyzing the Motion
This formula is for calculating revenue:
of a Projectile
R = px
Height of the projectile after X amount of time
is:
R = revenue
p= price
h (x) = -32x2 + X + HI
x = number of units sold
VI2
VI = Initial velocity
HI = Initial Height
Linear Regression on a calculator
To calculate linear regression on a calculator you must first
input the data, then using the QUADratic REGression button
obtain the results. This will give you a, b, and c but you must
plug them into the quadratic formula for the full answer
Recommended Problems for
3.4 are:
6, 7, 12, 28,29
3.5
Inequalities Involving
Quadratic Functions
•Graphing Inequalities
•Solution Set
Solution Set
Graphing a quadratic inequality is the same as graphing a regular
quadratic function except for that when graphing a quadratic
inequality you need to have a solution set
The solution set is calculated by either using the x – intercepts if
the graph is below the x – axis or points on the line g (x) (if the
inequality we are solving is f(x)
Recommended Problems for
3.5 are:
6, 13, 20, 21, 26, 32