5-Minute Check on Chapter 2

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5-Minute Check on Chapter 2

• Evaluate 42 - x - 7 if x -3
• Find 4.1 ? (-0.5)
• Simplify each expression
• 3. 8(-2c 5) 9c
  4. (36d 18) / (-9)
• A bag of lollipops has 10 red, 15 green, and 15
  yellow lollipops. If one is chosen at random,
  what is the probability that it is not green?
• Which of the
  following is a true statement

Standardized Test Practice
8/4 lt 4/8
-4/8 lt -8/4
-4/8 gt -8/4
-4/8 gt 4/8
A
C
B
D
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Lesson 10-4

• Solving Quadratic Equations by Using the
  Quadratic Formula

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Transparency 4
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Objectives

• Solve quadratic equations by using the Quadratic
  formula
• Use the discriminant to determine the number of
  solutions for a quadratic equation

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Vocabulary

• Quadratic formula
• Discriminant

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Working Backwards

• Start with the answer
• Undo the operation that got you to the answer
• Keep undoing until you get back to the beginning

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Example 1
Method 1 Factoring
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Example 1 cont
Method 2 Quadratic Formula
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Example 1 cont
Answer The solution set is 5, 7.
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Example 2
Step 1 Rewrite the equation in standard form.
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Example 2 cont
Step 2 Apply the Quadratic Formula.
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Example 2 cont
Check the solutions by using the CALC menu on a
graphing calculator to determine the zeros of the
related quadratic function.
Answer The approximate solution set is 0.3,
0.8.
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Example 3
Space Travel Two possible future destinations of
astronauts are the planet Mars and a moon of the
planet Jupiter, Europa. The gravitational
acceleration on Mars is about 3.7 meters per
second squared. On Europa, it is only 1.3 meters
per second squared. Using the information and
equation from Example 3 on page 548 in your
textbook, find how much longer baseballs thrown
on Mars and on Europa will stay above the ground
than a similarly thrown baseball on Earth.
In order to find when the ball hits the ground,
you must find when H 0. Write two equations to
represent the situation on Mars and on Europa.
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Example 3 cont
Baseball Thrown on Mars
Baseball Thrown on Europa
These equations cannot be factored, and
completing the square would involve a lot of
computation.
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Example 3 cont
To find accurate solutions, use the Quadratic
Formula.
Since a negative number is not reasonable, use
the positive solutions.
Answer A ball thrown on Mars will stay aloft 5.6
2.2 or about 3.4 seconds longer than the ball
thrown on Earth. The ball thrown on Europa will
stay aloft 15.6 2.2 or about 13.4 seconds
longer than the ball thrown on Earth.
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Example 4a
Answer The discriminant is 220. Since the
discriminant is negative, the equation has no
real roots.
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Example 4b
Step 1 Rewrite the equation in standard form.
Step 2 Find the discriminant.
Answer The discriminant is 0. Since the
discriminant is 0, the equation has one real
root.
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Example 4c
Step 1 Rewrite the equation in standard form.
Step 2 Find the discriminant.
Answer The discriminant is 244. Since the
discriminant is positive, the equation has two
real roots.
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Summary Homework

• Summary
• The solutions of a quadratic equation in the form
  ax2 bx c 0, where a ? 0, are given by the
  Quadratic Formula
• Homework
• pg

-b vb² - 4ac x ---------------------
-- 2a