Section 5.2 Introduction to Solving Quadratic Equations

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Section 5.2Introduction to Solving Quadratic
Equations

• Objectives Solve quadratic equations by taking
  square roots.
• Use the Pythagorean Theorem
  to solve problems involving right triangles.
• Standard 2.8.11.N. Solve quadratic equations.

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Solving Equations of the Form x2 a

• If x2 a and a gt 0, then
• x or x -
• or simply x

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I. Properties of Square Roots

• Product Property of Square Roots
  If a 0, and b 0
• Quotient Property of Square Roots If
  a 0 and b gt 0

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Example 1
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Example 2

• Solve 5x2 19 231. Give exact solutions.
  Then give approximate solutions to the nearest
  hundredth.

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Example 3 4
Solve 9(x - 2)2 121
Solve 4(x2)2 49
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A rescue helicopter hovering 68 feet above a
boat in distress drops a life raft. The height
in feet of the raft above the water can be
modeled by h(t) -16t2 68, where t is the
time in seconds after it is dropped. After how
many seconds will the raft dropped from the
helicopter hit the water?
When the raft hits the water, the height will
0, so h(t) 0
Since only positive values of time make sense,
the answer is 2.1 seconds.
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II. Pythagorean Theorem

• If ?ABC is a right triangle with the right angle
  at C, then a2 b2 c2.
• When you apply the Pythagorean Theorem, use the
  principal square root (positive square root)
  because distance and length cannot be negative.

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Ex 1. Find the unknown length in each right
triangle. Give answers to the nearest tenth.

• a. b.
• (5.1)2 (2.5)2 z2 p2 (4)2 (8.2)2
• 32.26 z2 p2 51.24
• 5.7 z p 7.2
• c. d.

y 8.1
r 9.3
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• Homework
• Integrated Algebra II- Section 5.2 Level A
• Honors Algebra II- Section 5.2 Level B