# 2.1 - Working with Quadratic Functions. GOODBAD VERY NOT Heres a trick to help you with the signs when you are multiplying two integers! + + - -

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2.1 - Working with Quadratic Functions

GOODBAD VERY NOT Heres a trick to help you with the signs when you are multiplying two integers! + + - -

A picture of Madison that is 10cm by 15cm is going to have a matting of uniform width around it inside of its frame. Determine a simplified expression for the area of the glass needed to cover the picture and matting. 2x+10 2x+15

Area = length x width Area = (2x+10)(2x+15) To simplify algebraic expressions we use the distributive property. This means that we multiply everything inside of the second brackets by everything that is inside the first brackets!

Strategy #1 – Make a chart Area = (2x+10)(2x+15) 2x+10 2x +15 4x 2 +150 +30x +20x Area = 4x 2 +50x +150

Strategy #2 – Algebra Tiles Area = -x 2 x x -x +1 x x x x +1 x x x x x2x2 x2x2 x2x2 x2x2 x2x2 x2x2 x2x2 x2x2 x x x x x x x x x x x x x x x x x x x x (2x+3)(2x+2)

Strategy #3 – FOIL FO IL IRST UTSIDE NSIDE AST Area = (2x+10)(2x+15) Area = 4x 2 +30x+20x +150 Area = 4x 2 +50x+150

Example: Expand and simplify a) b) c)

Homework: P AGE 85 #2, 3, 5 – 14