chapter 5 section 1 graphing quadratic functions
TRANSCRIPT
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Chapter 5Section 1Graphing Quadratic Functions
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Graphing Quadratic Functions (just read)Objective:
You will be given 2 forms of quadratic functions.
Based on the form, you will learn how to graph a quadratic function.
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What is a Quadratic Function?Definition Graph
• Has an “x2” in the equation
• Takes the shape of a “U” called a parabola
• Can “smile” or “frown”
• The lowest or highest point is the vertex
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Form #1: Standard FormWhat it looks like The impact of a
y = ax2 + bx + c
a, b, and c are numbers
a cannot equal zero
• If a is positive, then the parabola opens upwards (smile)
• If a is negative, then the parabola opens downwards (frown)
• If a is a fraction, parabola will be “wide”
• If a is a whole number not equal to 1, parabola will be “skinny”
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Let’s look at a few examples on the graphing calculator
y = x2 + 3x – 1 y = -x2 + x – 4
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Let’s look at a few examples on the graphing calculator
y = ½x2 + x – 1 y = -¾x2 – 4
y = 3x2 + x – 3 y = -2x2 + 2x - 5
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Vertex:
a
bx
2
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Vertex
To find the vertex:Step 1: write down a and b Step 2: plug into formula and get value – THIS IS THE X-COORDINATE!!!Step 3: take that value and plug into equation to get y
Now you have the vertex (x, y)
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Example
Find the vertex of y = 2x2 – 8x + 6.a =
b =
x =
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Let’s go our book…..
Page 253 Complete 20-25DIRECTIONS: find the vertex only!!!
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How to graph a quadratic functionStep 1: Write down the characteristics of
the function.Step 2: Find the vertex. Plot it!Step 3: Choose two more x-values one more
and one less than the vertex.
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Example:
X Y
32 2 xy
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Practice on your own
•Let’s graph 20 – 24. •Use the vertex you found and plot.•Find two more points and plot.
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Quadratic Functions Day 2Warm-UpReview HomeworkRecapWord Problems and partner activityNotes on graphing in Intercept FormGroup Activity
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Warm up: y = -½x2 + 4x - 4
X Y
3 3.5
4 4
5 3.5
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Homework Review
http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/Properties%20of%20Parabolas.pdf
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Notes…Real-life applicationThe engine torque y (in foot-pounds) of one
model of car is given by y = -3.75x2 + 23.2x + 38.8
Where x is the speed of the engine (in thousands of revs per minute).
1.Find the engine speed that maximizes torque.
2.What is the maximum torque?(revs per minute, torque)
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What are the characteristics of this quadratic?The engine torque y (in foot-pounds) of one
model of car is given by y = -3.75x2 + 23.2x + 38.8
Faces DownWide
This is why the question asks for the maximum. The vertex will give:
x = max revolutions, and y = max torque.
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Real-Life Application continued
Use the vertex formula to answer the questions…
a = -3.75
b = 23.2
x =
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Partner Activity
•Choose a partner•1 person is the writer•1 person is the reported (to me)•You need a piece of paper •Complete page 255 #55 a and b only!!!•Round your answers to the nearest
whole number
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Recap:
•A parabola that “smiles” or faces upwards (where a is a positive number) it will have a minimum.
•A parabola that “frowns” or faces downwards (where a is a positive number) it will have a maximum.
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Form #2: Intercept FormReview of Intercepts Characteristics of quadratics
Recall: An intercept is where are graph crosses the x or y axis
(x, 0) is the point – this is called the x-intercept
• Parabolas have either none, one, or two x-intercepts
• Intercept form looks like a factored equation
• Intercept form looks like: y = a(x – p)(x – q)
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Graphing in Intercept FormSteps: Ex: y = (x - 2)(x + 2)
Set each binomial equal to zero and solve for x. These will give you the intercepts.
x - 2 = 0 x + 2 = 0 + 2 +2 - 2 -2_______ _________x = 2 x = -2(2, 0) (-2, 0)
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Graphing in Intercept FormSteps: Ex: y = (x - 2)(x + 2)
Plot these points.The vertex is halfway between
these points. To find this: (p + q)/2 This is the x-
coordinate of the vertex!(-2 + 2)/2 = o/2 = 0Plug in x-coordinate to get y. y = (0 – 2)(0 + 2) y = (-2)(2) y = -4 so (0, -4)Plot vertex and draw the
parabola
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Let’s try together…..y = -(x – 3)(x + 1) y = 2x(x – 4)
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Group Assignment on notecardsWithin your group Assignment
One person is the writer/recorder
One person is the reporter
All work together on answering the questions!!!
• You are given 3 notecards
• Each problem needs to be on graph paper
• All three points must be labeled (intercepts and vertex)
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Homework
•Page 254 32, 33, 34, 36
http://olp.classzone.com/materials/2612962/M2C05AGD.PDF