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Objectives: Solve quadratic equations by finding square roots. Use quadratic models. Give a man a fish, and he'll eat for a day. Give a fish a man, and he'll eat for weeks! Takayuki Ikkaku, Arisa Hosaka and Toshihiro Kawabata Standard Form Linear Equation Ax + By = C A quadratic equation can be written in the standard form; ax2 + bx +c = 0 AX2 + BX +C = 0 a, b, and c are called? a is the leading coefficient coefficients Quadratic equations are equations where the highest power of the variable is 2. Which equations are quadratic? 2. 3x2 + 2x + 5 = 0 yes yes 5z2 + 5z = -3 3. x2 = 2 yes 4. y2 + y = y3 no 5. 4x + 2x = 0 6. y=3 1. no no How do we solve a quadratic of the form x2 = d? x 9 2 x 9 x 3 2 1. x2 = 4 2. x2 = 5 3. x2 4. x2 = -1 =0 x=2 Two solutions x = √5 Two solutions x=0 One solution No solutions Solve 3x2 -48 = 0 3x 48 0 2 3x 48 2 x 16 x 4 2 d = rt can be used to model problems with constant speed. The height of a falling object can be modeled using h = -16t2 + s where s is the height in feet from which the object was dropped and t is the number of seconds it has fallen. If you were to drop a watermelon from the top of a 200 ft building, how long would it take to hit the ground? h = -16t2 + s 0= -16t2 + 200 height when hits the ground -200 = -16t2 200 ft 12.5 = t2 √12.5 = t 3.54 t starting height page 461 9-32 all