Post on 04-Jan-2016
Solve: The length of a rectangular picture frame is 4 inches less than its width. The area of the picture frame is 320 square inches. Find the dimensions of the picture frame.
Review: 6.5i Mini-Quiz
Class Greeting
Objective: Students will solve real world problems involving quadratic equations. (continued)
Solving real world word problems involving Quadratic Equations
(continued)Chapter 6 – Factoring and Solving Equations
Section 5j
Example
Find the number of video games needed to be sold to have a profit of $30 by solving the equation by factorization.
30 = -0.4x2 + 8x – 10
0.4x2 – 8x + 40 = 0 4x2 – 80x + 400 = 0 x2 – 20x + 100 = 0
(x – 10)2 = 0 x = {10}
Answer: 10 video games need to be sold for a profit of $30.
x2 – 20x + 100 = 0
0.4x2 – 8x + 10 = -30Switch sides and change all the signs.Switch sides and change all the signs.Add 30 to both sides.Switch sides and change all the signs.Add 30 to both sides.Multiply everything by 10.
Switch sides and change all the signs.Add 30 to both sides.Multiply everything by 10.Divide everything by 4.
P = ?
Standard Form: Ax2 + Bx + C = 0
Preview 370/67
e. Find the number of video games needed to be sold to have a profit of $20 by solving the quadratic equation.
a. Find the standard form of the equation. Ax2 + Bx + C = 0
d. Find the x-intercepts of the graph.
b. Make an (x , y) table. c. Graph the ordered pairs (x , y).
Preview 371/69a
Preview 371/69b(b) Use the following formula for the sum of the first natural numbers to verify your answers to part (a). 1 + 2 + 3 + . . . + = ( + 1)
In part (a), was 5, 8, and 10. You can do those for homework.
(a) 1 + 2 + 3 + 4 = is 4 and ( + 1) is ( + 1) which is 10.
Example
(c) Use the following formula in part (b) to find if the sum of the first natural numbers is 171. 1 + 2 + 3 + . . . + = ( + 1)
Preview 371/69c(c) Use the following formula in part (b) to find if the sum of the first natural numbers is 210. 1 + 2 + 3 + . . . + = ( + 1)
You can do this for homework.
Example
171 = ( + 1)
342 = ( + 1)
2[ ] ]2 [ 2 – 342 = 0
Factor: 2 – 342 = 0 ( + 19)(
𝑛=\{−19 , 18\}𝑛={18 }must be positive
Homework
370 + 371/67 and 69
Lesson Summary: Objective: Students will solve real world problems involving quadratic equations. (continued)
Preview of the next Lesson: Objective: The students will correct their practice test on sections 6-4 and 6-5.