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

Class Greeting

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

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

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.

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:

Example 1 – Mountain Biker’s Speed continued Equation: 5x2 – 20x = 25x + 25x – 100 5x2 – 70x + 100 = 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).

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

Example 1 – Mountain Biker’s Speed continued The biker’s speed coming down the trail is 7 + 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.

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

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

Do not round your answers. Homework 572/ 69-73 odd Do not round your answers. Leave your answers as square roots.

Stand Up Please