5.5 Quadratic Equations (Day 1)

Standard form of a quadratic equation ax2 + bx + c = 0, where a ≠ 0 Zero-Product Property For every real number a and b, if , ab = 0 then or . a = 0 b = 0 EX 1 (x + 5)(5x – 6) = 0 x + 5 = 0 or 5x – 6 = 0 Short cut: x = or - 5 5x = 6 { , } - 5 x = 5

( )( ) + – ( )( ) + + { , } { , } ( )( ) ( )( ) – – + – { , } { , } Solving by Factoring White Boards Together L 1. s2 – 3s – 10 = 0 2. h2 + 10h = – 21 1, 10 L ( )( ) s + – 2 s 5 = 0 2, 5 h2 + 10h = 0 + 21 1, 21 ( )( ) + + 3, 7 h 3 h 7 = 0 + 2s = OI √ – 5s – 3s √ OI √ 7h + 3h = 10h √ { , } – 2 5 { , } – 3 – 7 F L F L 3. 5s2 – 17s = – 6 4. 4r2 = r + 3 1, 5 1, 6 1, 4 1, 3 5s2 – 17s = 0 + 6 4r2 = 0 – r – 3 2, 3 2, 2 ( )( ) ( )( ) 1 s – 3 5 s – + 2 = 0 4 r 3 1 r – 1 = 0 OI √ – 2s – 15s = – 17s √ OI √ – 4r + 3r = – 1r √ { , } { , } 3 1 5 4

White Boards OI √ – 5x – 6x = – 11x OI √ – 6x + 7x = 1x Solving by Factoring White Boards OI √ – 5x – 6x = – 11x √ OI √ – 6x + 7x = 1x √

Solving using square roots: Together White Boards

5.5 Quadratic Equations (Day 2)

Solving by Factoring 1. 3x2 – 20x – 7 = 0 2. 2x2 + 7x – 5 = 0 White Boards 1. 3x2 – 20x – 7 = 0 2. 2x2 + 7x – 5 = 0

Solving by Graphing Enter 2x2 + 7x – 5 into Y1 and graph the function. Use a graphing calculator to solve 2x2 + 7x – 5 = 0. Round the solutions to the nearest hundredth. Enter 2x2 + 7x – 5 into Y1 and graph the function. Use CALC to find the two zeros.

Solving by Graphing 4. x2 + 3x – 6 = 0 5. 2x2 + 4x = 11 White Boards Give your answers to at most two decimal points. 4. x2 + 3x – 6 = 0 5. 2x2 + 4x = 11

Real-World Connection The function y = -16x2 + 270 models the height y in feet of a heavy object x seconds after it is dropped from the top of a building that is 270 feet tall. How long does it take the object to hit the ground?

Real-World Connection A carpenter wants to cut a piece of plywood in the shape of a right triangle. The carpenter wants the hypotenuse of the triangle to be 6 feet long and the legs be as shown in the diagram. About how long should the perpendicular sides be? 6 ft. x + 1 x