7-1 EXPLORING QUADRATIC FUNCTIONS MISS BATTAGLIA – ALGEBRA 1 CP OBJECTIVE: GRAPH QUADRATIC...

7-1 E

XPLORIN

G

QUADRATIC

FUNCTI

ONS

MI S

S B

AT T A

GL I A

– A

L GE

BR

A 1

CP

OB

J EC

TI V

E:

GR

AP

H Q

UA

DR

AT

I C F

UN

CT

I ON

S O

F

TH

E F

OR

M Y

=A

X^

2

REAL WORLD APPLICATIONS - QUADRATICS• Throwing a ball

• Bicycling up and down a hill

• Calculating Speed (Example: Avid kayakers, use quadratic equations to estimate their speed when going up and down a river)

WARM UP – WORK WITH A PARTNERUse a graphing calculator.

1. a. Graph the equations and .

b. How are the graphs in part (a) alike? different?

2. a. Graph the equations and .

b. How are the graphs in part (a) different from the graphs in Question 1? How are they like the graphs in Question 1?

WHAT IS SYMMETRY?

http://www.superteacherworksheets.com/geometry/symmetry-2_TZTDQ.pdf

QUADRATIC FUNCTIONS

The graphs from the warm up are all parabolas. If you draw a parabola on a piece of paper, you can fold the paper down the middle of the parabola and the two sides will match exactly. The line down the middle of the parabola is the axis of symmetry.

DRAW THE AXIS OF SYMMETRY

QUADRATIC FUNCTION

For a ≠ 0, the function is a quadratic function.

Ex: , ,

When a quadratic function is written in

the form , it is in standard form.

EXAMPLEName the values of a, b, and c for each quadratic

equation.

a. b.

Write each quadratic function in standard form.

a. b.

MAKE A TABLE OF VALUES & GRAPH THE QUADRATIC FUNCTIONS

and

x 2x2 -2x2

-2

-1

0

1

2

The highest or lowest point on a parabola is called the vertex of the parabola.

When a parabola opens upward, the y-coordinate of the vertex is the minimum

value of the function.

When a parabola opens downward, the y-

coordinate of the vertex is the maximum value of

the function.

EXAMPLE

Answer these questions for and

a.What is the value of a?

b.In which direction does each graph open?

c.Is the y-coordinate of the vertex a minimum or a maximum value of the function?

USE A GRAPHING CALCULATOR

Graph . Compare the widths of the graphs.

EXAMPLE

Order each group of quadratic functions from widest to narrowest graph.

y = 2x2, y = 3x2, y = -5x2

HOMEWORK

Pg 321 # 2 – 4 , 6, 7, 9, 11, 12