Today

1
Todays Objective

• To be able to SKETCH the graph of a quadratic
  equation.
• Take Notes when you see this icon.

2
Quadratic Functions

• Quadratic functions are equations of the form ..
• y ax2 bx c
• Where a, b, and c are real numbers and a is not
  zero.

3
Quadratic Functions

• y ax2 bx c

And Finally the whole
Then comes the x term
x2 term is always first
4
Find the values for a, b, and c in the following

• 1.) y 2x2 -5x 12
• a 2, b -5, c 12
• 2.) y 6 - x2 3x
• 2.) y - x2 3x 6
• a -1, b 3, c 6

5
Quadratic Functions

• The graph of a quadratic function is U shaped
  and is called a parabola.
• The end of the parabola is called the Vertex.

6
Quadratic Functions

• The line the U is wrapped around is called the
  Axis of Symmetry.

7
Consider the graph of y x2
Parabola
Y
X
Axis of Symmetry
Vertex (0,0)
8
Quadratic Equations of the form y ax2 bx c

• 1.) If a is positive, the U is up.
• 2.) If a is negative, the U is down.
• 3.) The Vertex has an x-coordinate of -b/2a.

9
Now Lets Graph y x2 - 2x - 3

• 1.) Find the Vertex
• 2.) Make a T-Table.
• 3.) Pick 5 x values that are small, some
  negative, and dont forget 0.

10
Graphing Quadratic Functions

• y x2 - 2x - 3
• Find the Coordinate of the Vertex.
• -b/2a x coordinate
• -(-2)/2(1)
• 2/2 1

Now find y
(1,?)
11
Graphing Quadratic Functions

• y x2 - 2x - 3
• Plug in the x (1) value
• y (1)2 -2(1) - 3
• y 1 - 2 -3
• y -4

(1,-4)
12
y x2 - 2x - 3
Now we will plug them into the equation
x
y
-3
-1
0
The vertex
1
3
13
y x2 - 2x - 3

• y (-3)2 - 2(-3) - 3

• y 9 6 - 3
• y 12

12
14
y x2 - 2x - 3

• y (-1)2 - 2(-1) - 3

• y 1 2 - 3
• y 0

12
0
15
y x2 - 2x - 3

• y (0)2 - 2(0) - 3

• y - 3

12
0
-3
16
y x2 - 2x - 3

• y (1)2 - 2(1) - 3

• y 1 - 2 - 3
• y -4

12
0
-3
-4
17
y x2 - 2x - 3

• y (3)2 - 2(3) - 3

• y 9 - 6 - 3
• y 0

12
0
-3
-4
0
18
y x2 - 2x - 3
Y
X
Vertex (1,-4)
19
Graphing Quadratic Functions

• y x2 - 6x 8 and
• y 2(x2 - 6x 8)
• Then find the vertex of each
• (3,-1) and (3,-2).

20
Rewrite each equation in standard form ..

• 1.) 9 2x2 -5x 12
• 0 2x2 -5x 3
• 2.) 3 6 - x2 3x
• 0 - x2 3x 3