ALGEBRA I - SECTION 9-4 (Factoring to Solve Quadratic Equations) @ SECTION 9-4 : FACTORING to SOLVE QUADRATIC EQUATIONS

QUADRATIC EQUATION : An equation of the form ax2 + bx + c = 0 Equations like x2 – 2x – 8 = 0, x2 – 36 = 0, and 4x2 + 3x – 1 = 0 are examples of quadratic equations. 1) If ab = 0, what do you know about a and/or b? ANSWER : Either a = 0, b = 0, or both a and b = 0.

ZERO PRODUCT PROPERTY : If ab = 0. then a = 0, b = 0, or a = b = 0. Solve by factoring. 2) 3x(x – 1) = 0 Make sure one side = 0. DONE!!! 3x = 0 x – 1 = 0 Set each factor with a variable = 0. Solve each equation.

3) w(3w + 5) = 0 ANSWERS : 0, -5/3 Hmm….what do we have to do first? 4) x2 + 4x – 12 = 0 (x + 6)(x – 2) = 0 x + 6 = 0 x – 2 = 0 x = -6 x = 2

5) y2 – 3y = 0 ANSWERS : 0, 3 6) a2 – 11a = -28 Be careful!! ANSWERS : 4, 7 7) 6r2 – 11r = 35 ANSWERS : -5/3, 7/2 8) 4c2 = -19c + 5 ANSWERS : -5, 1/4 9) 5m2 = m ANSWERS : 0, 1/5

10) The length of Austin’s pet rectangle is 4 feet less than three times its width. The area of the rectangle is 55 square feet. Find the dimensions of Austin’s rectangle. 5 by 11 feet 11) Mark kicks a ball up in the air. The height, h, in feet, of the ball t seconds after it has been kicked is given by the equation, h = -16t2 + 8t + 4. How long after Mark has kicked the ball will it be 4 feet above the ground? 0 and 0.5 seconds