The Quadratic Formula

1
The Quadratic Formula
ALGEBRA 2 LESSON 5-8
Use the Quadratic Formula to solve 3x2 23x
40 0.
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2
The Quadratic Formula
ALGEBRA 2 LESSON 5-8
(continued)
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3
The Quadratic Formula
ALGEBRA 2 LESSON 5-8
Solve 3x2 2x 4.
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4
The Quadratic Formula
ALGEBRA 2 LESSON 5-8
The longer leg of a right triangle is 1 unit
longer than the shorter leg. The hypotenuse is 3
units long. What is the length of the shorter leg?
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5
The Quadratic Formula
ALGEBRA 2 LESSON 5-8
(continued)
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6
The Quadratic Formula
ALGEBRA 2 LESSON 5-8
Determine the type and number of solutions of
x2 5x 10 0.
a 1, b 5, c 10 Find the values of a, b,
and c.
b2  4ac (5)2 4(1)(10) Evaluate the
discriminant.
25 40 Simplify.
15
Since the discriminant is negative, x2 5x 10
0 has two imaginary solutions.
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7
The Quadratic Formula
ALGEBRA 2 LESSON 5-8
A player throws a ball up and toward a wall that
is 17 ft high. The height h in feet of the ball t
seconds after it leaves the players hand is
modeled by h 16t 2 25t 6. If the ball
makes it to where the wall is, will it go over
the wall or hit the wall?
Since the discriminant is negative, the equation
17 16t2 25t 6 has no real solution. The
ball will hit the wall.
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