1. Review: 10.3a Mini-Quiz
Solve by using the Quadratic Formula.

2. Class Greeting

3. Chapter 10 Quadratic Equations and Functions
Lesson 10-3b
Solving Quadratic Equations
by Using the Quadratic Formula

4. Objective: Students will solve word problems by involving quadratic equations using the quadratic formula.

5. Example 1 – Mountain Biker’s Speed
A mountain biker spends a total of 5 hours going up a
25-mile mountain trail and coming back down. The biker’s
speed up the trail is 4 miles per hour less than the speed
down the trail. What is the biker’s speed coming down the
trail?
Solution
Form a verbal model for the total time. Remember that
Distance = Rate  Time.
So,
Time = Distance  Rate.
Speed = Rate, they are synonymous.

6. Example 1 – Mountain Biker’s Speed
continued
Let x represent the speed coming down the trail.
Let x – 4 represent the speed going up the trail.
Verbal Model:
Labels: Total time = 5 (hours)
Time up = (hours)
Time down = (hours)
Equation:

7. Example 1 – Mountain Biker’s Speed
continued
Equation:
5x2 – 20x = 25x + 25x – 100
5x2 – 70x = 0
x2 – 14x + 20 = 0
This equation does not factor, so use the Quadratic Formula to solve the equation.
Multiply each side by LCD x(x – 4).

8. Example 1 – Mountain Biker’s Speed
continued
x2 – 14x + 20 = 0
Substitute a = 1, b = –14 and c = 20.

9. Example 1 – Mountain Biker’s Speed
continued
The biker’s speed coming down the trail is
miles per hour.
The solution 7 – is excluded because the uphill
rate x – 4 would be negative and therefore the time going uphill would be negative which is impossible.
Check the solution in the original statement of the problem.

10. Lesson Summary: Objective: Students will solve word problems by involving quadratic equations using the quadratic formula.

11. Preview of the next Lesson: Objective: The students will complete a practice test on sections 10-1 to 10-3 individually in class.

12. Do not round your answers.
Homework
572/ odd
Do not round your answers.
Leave your answers as square roots.

13. Stand Up Please