Algebra Period 3 (Monday)

Radical Equations with Quadratics 13-6

THIS IS A REVIEW OF CHAPTER 11!!!

You square both sides to get rid of the radical sign
For these problems, you'll get a quadratic on one side after you square
BE SURE TO CHECK BOTH ANSWERS TO MAKE SURE THEY BOTH CHECK!

WORD PROBLEMS WITH QUADRATICS 13-7
There are 2 major types: Frame problems, triangle problems

FRAME PROBLEMS:
You know the frame's dimensions and the picture's area inside. You need to find the width of frame.
1)Set x = width of the frame
2) Write the area formula using the dimensions given in the problem minus 2x
as the base and height of the area of the picture.
Why are we subtracting 2x? Because there are two widths, one on the top and one on the bottom, one on the right side and one on the left side
3) Set this product equal to the area of the picture given in the problem
EXAMPLE:
A picture frame is 20 cm by 12 cm. The picture has an area of 84 cm²
(20 - 2x)(12 - 2x) = 84
FOIL
240 - 40x - 24x + 4x² = 84
Combine like terms and bring the 84 over
4x² -64x + 240 - 84 = 84 - 84
4x² - 64x + 156 = 0
Divide by 4 on each side
x² - 16x + 39 = 0
FACTOR or use the QUADRATIC FORMULA
(x - 3)(x - 13 ) = 0
x = 3 cm or x = 13 cm
The 13 cm does not make sense! How can the width of the frame be more than one of its dimensions (the height was only 12 cm!!!)???
Therefore, the only answer is that the frame is 3 cm wide.

The right triangle example in the book on p. 603 uses the Pythagorean Theorem