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.