9.6 THE QUADRATIC FORMULA:Quadratic Formula: Formula used to find the solution(s) of any quadratic equation.
2 42
b b acx
a
If ax2+bx+c = 0 and a ≠ 0,then
GOAL:
QUADRATIC EQUATION:
Ex: What are the solutions to? Use the quadratic formula.
x2-8=2x
SOLUTION: We must first put the equation in ax2+bx+c=0 form.
a = 1 , b = -2 and c = -8 x2-8=2x x2-2x-8 =0
2 42
b b acx
a
22 2( ) ( ) 4( )( 8
2( )1)1
x
2 4 322
x
2 362
x
2 62
x
2 6 42 2
2x
2 6 82
42
x
x = -2, 4
YOU TRY IT:
Ex: What are the solutions to? Use the quadratic formula.
x2-4x=21
SOLUTION: We must first put the equation in ax2+bx+c=0 form.
a = 1 , b = -4 and c = -21 x2-4x=21 x2-4x-21 =0
2 42
b b acx
a
24 4( ) ( ) 4( )( )
21
)21
1(x
4 16 842
x
4 1002
x
4 102
x
4 10 62 2
3x
4 10 142 2
7x
x = -3, 7
REAL-WORLD:
In the shot put, An athlete throwsA heave metal ballThrough the air. The arc of the ball is modeled by the equation: -0.04x2+.84x+2. Where x is the horizontal distance. How far from the athlete will the ball land?
SOLUTION: The given equation is already in standard form:
a = -0.04 , b = 0.84 and c = 2 -0.04x2+0.84x+2 = 0
2 42
b b acx
a
2( ) ( ) 4 00. .04
0.84 0.8 ( )( )
2( )04 24
x
0.84 1.02560.08
x
0.84 1.0130.08
x
0.84 1.0130.08
23.16x
x cannot be negative: x = 23.16 meters
0.84 1.0130.08
2.16x
VIDEOS: SOLVING BY
FACTORING Solving by factoring:
http://www.khanacademy.org/math/algebra/quadratics/factoring_quadratics/v/Example%201:%20Solving%20a%20quadratic%20equation%20by%20factoring
VIDEOS: SOLVING BY
FACTORING Solving by factoring:
http://www.khanacademy.org/math/trigonometry/polynomial_and_rational/quad_formula_tutorial/v/solving-quadratic-equations-by-completing-the-square
http://www.khanacademy.org/math/algebra/quadratics/factoring_quadratics/v/Example%202:%20Solving%20a%20quadratic%20equation%20by%20factoring
CLASSWORK:
Page 508-509:
Problems: 4, 7, 15, 21, 25, 36, 37.
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