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Alg 2X - Unit 4
Day 2 – Graphing Quadratic Functions (Again) and Using the Calculator
Goal: To use your calculator to graph quadratics and solve word problems
Thinking Skill: Examine information from more than one point of view.
BUT FIRST … more factoring review. FACTOR EACH EXPRESSION COMPLETELY.
(This means take out the GCF if there is one;
then look for Difference of Two Squares, Easy Trinomial Factoring or a British Method Opportunity.)
1. 64y2 – 16
2. 4x2 – 12x – 40
3. 15x2 -7x -2
4. a2bx2 –a2by2
5. x2 + x - 30
This is STANDARD form:
f(x) = ax2 + bx + c
Graphing from STANDARD form:
What do you REALLY NEED to know to graph? Only 3 things!!
#1. UP or DOWN (based completely on whether "a" is positive or negative)
#2. Vertex: Get x from x 
b
and then plug the x-value into the function to get y
2a
#3. y-intercept (based completely on "c" -- in fact, it is just "c"!)
What else is helpful to know (or what else might you be asked about?)
-- What is the Axis of Symmetry?
-- What is the "Symmetric Point"?
-- What is the MAX or MIN?
-- What are the x-intercepts (also called "roots" or "zeros")… more on that next week …
Example #1: Graph the following equation, given to you in STANDARD FORM:
f(x) = 3x2 + 12x + 8
Three Things You Really Need to Know to Graph:
What is the Axis of Symmetry? _______________
Does this graph have a MAX or a MIN? ______ At what point does it occur? _________
Example #2: Graph the following equation, given to you in STANDARD FORM:
f(x) = -2x2 -8x -5
Three Things You Really Need to Know to Graph:
What is the Axis of Symmetry? _______________
Does this graph have a MAX or a MIN? ______ At what point does it occur? _________
REVIEW OF VERTEX FORM:
Give the vertex of each parabola represented by the quadratic functions, ALL WRITTEN IN VERTEX FORM:
1. f ( x)  ( x  3)  2
2
Vertex: _____________
2. f ( x)  ( x  5)
2
Vertex: _____________
3. f ( x)  ( x  4)  7
Vertex: _____________
4. f ( x)  x  15
Vertex: _____________
2
2
5. f ( x)  ( x  212)  336
2
Vertex: _____________
USING YOUR CALCULATOR TO FIND A VERTEX (MAX OR MIN):
f(x) = 3x2 + 12x + 8
Press the “y=” button and enter the equation.
For this equation, the vertex is a __________________.
Therefore, choose: 2nd →CALC →3:minimum
Put the cursor on the LEFT side of the vertex and hit ENTER.
Move the cursor to the RIGHT side of the vertex and hit ENTER again.
(Then hit ENTER one more time to move through the "Guess" option)
The vertex, which is your minimum value, will appear on the screen as the x- and y-values.
WORD PROBLEM Example #1:
A record label uses the function a  t   90t 2  8100t to model the sales of a new release. The number of
albums sold is a function of time, t, in days. On which day were the most albums sold? What is the maximum
number of albums sold on that day? Window: -10, 100, 1, -20, 190000, 1
WORD PROBLEM Example #2:
An airline sells a 3-day vacation package. Sales from this vacation package can be modeled by the quadratic
function s( p)  40 p 2  32000 p . Sales are dependent on the price, p, of the package. If the price is set too
high, the package won’t sell, but if the price is too low, prospective buyers will think it is a scam. Window: 10, 800, 1, -20, 6500000, 1
a.) At what price, p, does the company have the greatest sales?
b.) What are the maximum sales possible based on this model?
Homework: p. 328: 15, 16, 20, 24-26, 30, 33a