Algebra 2 Notes
Name __________________
6.5 Use the Quadratic Formula and the Discriminant
Quadratic Equation:
Quadratic Formula:
For any quadratic equation in the form ax + bx + c = 0 , the quantity b ! 4ac is
called the ________________________ .
2
Quadratic
Equation
Discriminant
2
Nature of the
Roots
Related Graph and
Number of x-intercepts
3x 2 + 2x ! 8 = 0
!3x 2 + 5x + 5 = 0
x 2 ! 4x + 4 = 0
2x 2 + x + 1 = 0
~What do you notice about the value of the discriminant for a quadratic equation that
has 2 rational roots?
~What do you notice about the value of the discriminant for a quadratic equation that
has 2 irrrational roots?
~What do you notice about the value of the discriminant for a quadratic equation that
has 1 rational root?
~What do you notice about the value of the discriminant for a quadratic equation that
has 2 imaginary roots (0 real roots)?
Find the discriminant, describe the nature of the roots, and solve.
1.
3.
2x 2 + x ! 15 = 0
2.
2x 2 ! 9x + 8 = 0
5
4.
x 2 = 8x ! 16
7
x
2
+
4
7
=
2
7
x
Practice: On a separate sheet of paper, solve the following using the
Quadratic Formula. Be sure to include all 3 parts in your final answer.
1.
3.
5.
x 2 + 12x + 32 = 0
1
5
x2 + 1 =
2
5
x
2x 2 ! 11 = ! 7 x
2.
x 2 ! 4x + 1 = 0
4.
x 2 = 12x ! 42
6.
x 2 ! 16x + 4 = 0