1. 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 (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: A
8/4 < 4/8 B
-4/8 < -8/4 C
-4/8 > -8/4 D
-4/8 > 4/8
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2. Solving Quadratic Equations by Using the Quadratic Formula
Lesson 10-4
Solving Quadratic Equations by Using the Quadratic Formula

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4. Transparency 4a

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

6. Vocabulary
Quadratic formula –
Discriminant –

7. Working Backwards Start with the answer
“Undo” the operation that got you to the answer
Keep “undoing” until you get back to the beginning

8. Example 1 Use two methods to solve Method 1 Factoring
Original equation
Factor
Zero Product Property or
Solve for x.

9. Example 1 cont Method 2 Quadratic Formula For this equation,
Multiply.

10. Example 1 cont
Add.
Simplify. or
Answer: The solution set is {–5, 7}.

11. Example 2
Solve by using the Quadratic Formula. Round to the nearest tenth if necessary.
Step 1 Rewrite the equation in standard form.
Original equation
Subtract 4 from each side
Simplify.

12. Example 2 cont Step 2 Apply the Quadratic Formula. Quadratic Formula
a = 15, b = -8 and c = -4
Multiply,
then Add. or

13. 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}.

14. 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.

15. 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.

16. 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.

17. Example 4a
State the value of the discriminant for . Then determine the number of real roots of the equation.
and
Simplify.
Answer: The discriminant is –220. Since the discriminant is negative, the equation has no real roots.

18. Example 4b
State the value of the discriminant for . Then determine the number of real roots of the equation.
Step 1 Rewrite the equation in standard form.
Original equation
Add 144 to each side
Simplify.
Step 2 Find the discriminant.
a = 1, b = 24 and c = 144
Simplify.
Answer: The discriminant is 0. Since the discriminant is 0, the equation has one real root.

19. Example 4c
State the value of the discriminant for Then determine the number of real roots of the equation.
Step 1 Rewrite the equation in standard form.
Original equation
Subtract 12 from each side
Simplify.
Step 2 Find the discriminant.
a = 3, b =10 and c = -12
Simplify
Answer: The discriminant is Since the discriminant is positive, the equation has two real roots.

20. Summary & Homework Summary: Homework:
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 ± √b² - 4ac
x = 2a