1. Graphing Quadratic Functions
Chapter 5 Section 1
Graphing Quadratic Functions

2. 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.

3. 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

4. Form #1: Standard Form
What 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”

5. Let’s look at a few examples on the graphing calculator
y = x2 + 3x – 1 y = -x2 + x – 4

7. 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

8. Vertex:

9. 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)

10. Example
Find the vertex of y = 2x2 – 8x + 6. a = b = x =

11. Let’s go our book…..
Page 253 Complete DIRECTIONS: find the vertex only!!!

12. How to graph a quadratic function
Step 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.

13. Example: X Y

14. Practice on your own Let’s graph 20 – 24.
Use the vertex you found and plot.
Find two more points and plot.

15. Quadratic Functions Day 2
Warm-Up
Review Homework
Recap
Word Problems and partner activity
Notes on graphing in Intercept Form
Group Activity

16. Warm up:
y = -½x2 + 4x - 4 X Y 3
3.5 4 5

17. Homework Review
lg2Worksheets/Properties%20of%20Parabolas. pdf

18. Notes… Real-life application
The engine torque y (in foot-pounds) of one model of car is given by
y = -3.75x x
Where x is the speed of the engine (in thousands of revs per minute).
Find the engine speed that maximizes torque.
What is the maximum torque?
(revs per minute, torque)

19. What are the characteristics of this quadratic?
The engine torque y (in foot-pounds) of one model of car is given by
y = -3.75x x
Faces Down
Wide
This is why the question asks for the maximum. The vertex will give:
x = max revolutions, and
y = max torque.

20. Real-Life Application continued
Use the vertex formula to answer the questions… a = b = 23.2 x =

21. 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

22. 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.

23. Form #2: Intercept Form
Review 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)

24. Graphing in Intercept Form
Steps:
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 = _______ _________ x = 2 x = -2 (2, 0) (-2, 0)

25. Graphing in Intercept Form
Steps:
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 = 0 Plug 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

26. Let’s try together…..
y = -(x – 3)(x + 1)
y = 2x(x – 4)

27. Group Assignment on notecards
Within 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)

28. Homework
Page , 33, 34, 36
C05AGD.PDF