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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
