Transcript Section 3.1: Understanding Rational Exponents

Section 11.3:
Finding Complex Solutions
of Quadratic Equations
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Objective:
By following instructions, students will be able to:
1. Find the complex solutions of any quadratic
equation.
2
explain 1A
Solve the equation by completing the square. State whether the solutions are real
or non real.
3x  9 x  6  0
2
3
explain 1B
Solve the equation by completing the square. State whether the solutions are real
or non real.
x  2x  7  0
2
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Your-Turn #1
a)
Solve the equation by completing the square. State whether the
solutions are real or non real.
x 2  8 x  17  0
b)
x 2  10 x  7  0
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explain 2A
Answer the question by writing an equation and determining whether the solutions
of the equation are real or non-real.
A ball is thrown in the air with an initial vertical velocity of 14 m/s from an initial height of 2 m.
The ball’s height h (in meters) at time t (in seconds) can be modeled by the quadratic function
h(t )  4.9t 2  14t  2 .
Does the ball reach a height of 12 m?
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explain 2B
Answer the question by writing an equation and determining whether the solutions
of the equation are real or non-real.
A person wants to create a vegetable garden and keep the rabbits out by enclosing it with 100
feet of fencing. The area of the garden is given by the function
A( w)  w(50  w) where w is the width (in feet) of the garden.
Can the garden have an area of 700 square feet?
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Your-Turn #2
Answer the question by writing an equation and determining if the
solutions are real or non-real.
A hobbyist is making a toy sailboat. For the triangular sail, she wants the height h (in
inches) to be twice the length of the base b (in inches). Can the area of the sail be 10
square inches?
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explain 3A
Solve the equation using the quadratic formula. Check a solution by substitution.
 5x 2  2 x  8  0
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explain 3B
Solve the equation using the quadratic formula. Check a solution by substitution.
7 x 2  2 x  3  1
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Revisit Objective:
Did we…
1. Find the complex solutions of any quadratic
equation?
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HW:
Sec 11.3 pg 411 #s 1, 3-13, 22
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