Download Notes for Lesson 9-9: The Quadratic Formula and the Discriminant

Notes for Lesson 9-9: The Quadratic Formula and the Discriminant
9-9.1&2 – Using the Quadratic Formula
Last lesson we solved quadratic equation by completing the square. If we took the standard form of a quadratic
and solved it by completing the square, we would have solved it for x. That would give us a formula to use for
and quadratic equation.
That formula is : X 
 b  b 2  4ac
where a, b and c come from the quadratic.
2a
Examples: Solve using the quadratic formula.
2 x  3x  5  0
A  2, B  3, C  5
2
 3  32  4(2)(5)
X
2(2)
 3  9  40
4
 3  49
X
4
3 7
X
4
5
X   or1
2
X
2x  x2  3
0  x 2  2x  3
A  1, B  2, C  3
 (2)  (2)  4(1)(3)
2(1)
2
X
2  4  12
2
2  16
X
2
24
X
2
X  3or  1
X
x2  2x  4  0
A  1, B  2, C  4
X
 (2)  (2) 2  4(1)(4)
2(1)
2  4  16
2
2  20
X
2
X
9-9.3 – Using the Discriminant
Vocabulary:
Discriminant – the b 2  4ac in the quadratic formula that tells the number of solutions
The discriminant can be use to tell how many solutions there will be to a quadratic equation.
If b 2  4ac >0 then there will be 2 solutions because there are 2 square roots
If b 2  4ac =0 then there will be one solution because there is only 1 square root of zero
If b 2  4ac <0 then there will be no solution because negative numbers have no square roots
Examples: Find the number of solutions for each equation using the discriminant
3 x 2  10 x  2  0
10 2  4(3)(2)
100  24
76
2 solutions
Do Practice B #’s 2 – 12 even
9x 2  6x  1
x2  x 1  0
(6) 2  4(9)(1)
36  36
(1) 2  4(1)(1)
1 4
0
3
1 solution
No Solutions