Objectives:

1

• Objectives
• Be able to put a quadratic into standard form.
• Be able to find the vertex of a quadratic in
  standard form.
• Be able to graph a quadratic from the standard
  form.

Critical Vocabulary Quadratic Parabola Vertex Axi
s of Symmetry
Warm UP 1. Multiply (3x - 2)(x - 5) 2.
Multiply (2x2 - 3x - 5)(2x 3)
2
I. Standard Form of a Quadratic
Standard Form y ax2 bx c
Example 1 Put y 2(3x - 4)(2x 1) in standard
form.
y 2(6x2 - 5x - 4)
FOIL/BOX
y 12x2 - 10x - 8
Distribute
What are the values of a, b, and c?
Example 2 Put y 2(x 3)2 - 4 in standard
form.
y 2(x 3)(x 3) - 4
Rewrite the equation
y 2(x2 6x 9) - 4
FOIL/BOX
y 2x2 12x 18 - 4
Distribute
y 2x2 12x 14
Combine Like Terms
What are the values of a, b, and c?
3
II. Finding the Vertex and Axis of Symmetry of a
Quadratic
To find the x value of the vertex use the
formula
Find the y value of the vertex by substitution
(x into the original equation)
Example 3 Find the vertex of the quadratic y
x2 - 6x 5
1st Find the x-value
2nd Find the y-value
y (3)2 6(3) 5
y 9 6(3) 5
y 9 18 5
y -4
What is the vertex?
(3,-4)
What is the Axis of Symmetry?
x 3
4
Page 225-226 10-14, 24-28 (10 problems)
5
III. Graphing From Standard Form
Example 4 Graph the equation y -3x2 24x - 43
1st Find the vertex and Axis of Symmetry
y -3(4)2 24(4) - 43
y -3(16) 24(4) - 43
y -48 96 - 43
y 5
2nd Graph the vertex
(4, 5)
3rd Graph two more points on each side
of the vertex
x
2
5
6
3
y
2
2
-7
-7
4th Sketch the Graph
6
III. Graphing From Standard Form
Example 5 Graph the equation y -½x2 2x 1
1st Find the vertex and Axis of Symmetry
2nd Graph the vertex
3rd Graph two more points on each side
of the vertex
x
y
4th Sketch the Graph
7
Page 226 34 44 evens (6 problems)