Solving Quadratic Equations in Factored Form

1
Solving Quadratic Equations in Factored Form
10.4
Goal 1 Solve Quadratic Equations using
the zero-product
property Goal 2 Relate solutions to the roots
of the parabolic graph of the
equation.
2
Zero Product Property
For any Real numbers a and b, if ab 0, then
either a 0, b 0, or both a and b equal 0
If (x 2)(x 7) 0, then x 2 0 or x 7
0
3
Solve using the zero-factor theorem
3x(x 2) 0
4
Solve by using the zero factor theorem
(x 3)(x 4) 0
5
Solve by using the zero factor theorem
(x 3)2 0
6
Solve using the zero factor theorem
(3x 1)(x 2) 0
7
Solve using the zero factor theorem
(x 1)(4x 3)(x 5) 0
8
Solve using the zero factor theorem
(t ½)(2t 7) 0
9
Writing Quadratic Equations
A Quadratic equation of the form (x p)(x q)
0 has roots p and q
You can use this pattern to find a quadratic
equation for a given pair of roots
10
Write a quadratic equation with the following
roots. Write in the form ax2 bx c 0
where a, b, and c are integers
Roots are 3 and 4
11
Write a quadratic equation with the following
roots. Write in the form ax2 bx c 0
where a, b, and c are integers
What does the graph look like? Hint the
x-coordinate of the vertex is the average of the
x-intercepts.
12
Write a quadratic equation with the following
roots. Write in the form ax2 bx c 0
where a, b, and c are integers
What does the graph look like? Hint the
x-coordinate of the vertex is the average of the
x-intercepts.
Homework
p. 600 20-50e, 62, 66, 74, 80 (need graph paper)