Solving Quadratic Equations by Finding Square Roots Objective: Students will solve a quadratic equation by finding square roots.

Algebra Standards: 2.0 Students understand and use such operations as taking the opposite, reciprocal, raising to a power, and taking a root. This includes the understanding and use of the rules of exponents. 15.0 Students apply algebraic techniques to rate problems, work problems, and percent mixture problems. 23.0 Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.

is an equation that can be written in Vocabulary Quadratic Equation is an equation that can be written in the standard form ax + bx + c =0, where a ≠ 0. 2 If d > 0, then x = d has two solutions: x = 2 If d = 0, then x = d has one solutions: x = 0 2 If d < 0, then x = d has no real solutions. 2

Vocabulary when x = 3 when x = -3 when x = -3

a) p = 225 c) k = 15 x = 16 b) x = 16 p = 225 k = 15 | x | = 4 | p | = #1 Solve Quadratic Equations Solve each equation 2 2 2 a) p = 225 c) k = 15 x = 16 b) 2 2 2 x = 16 p = 225 k = 15 | x | = 4 | p | = 15 | k | = x = ±4 p = ±15 k = 2 2 d) e) x = -4 x = 0 No real solution x = 0

a) b) x + 7 = 16 3x – 10 = 65 -7 -7 +10 +10 x = 9 3x = 75 | x | = 3 x #2 Rewrite Before Finding Square Roots Solve each equation 2 2 a) b) x + 7 = 16 3x – 10 = 65 -7 -7 +10 +10 2 1 2 x = 9 3x = 75 3 3 | x | = 3 x = ±3 2 x = 25 | x | = 5 x = ±5

c) d) x + 7 = 5 (x + 1) = 16 -7 -7 (x + 1) = 16 x = -2 | x + 1 | = 4 #2 Rewrite Before Finding Square Roots Solve each equation 2 2 c) d) x + 7 = 5 (x + 1) = 16 -7 -7 2 (x + 1) = 16 2 x = -2 | x + 1 | = 4 No solution x + 1 = 4 x + 1 = -4 -1 -1 -1 -1 x = 3 or x = -5

e) (a – 4) = 81 (a – 4) = 81 | a – 4 | = 9 a – 4 = 9 a – 4 = -9 +4 +4 #2 Rewrite Before Finding Square Roots Solve each equation 2 e) (a – 4) = 81 2 (a – 4) = 81 | a – 4 | = 9 a – 4 = 9 a – 4 = -9 +4 +4 +4 +4 a = 13 or a = -5

For a falling object, you can estimate/find the height of it. Falling Object Model For a falling object, you can estimate/find the height of it. 2 h = -16t + s h = height of the object in feet (ft) 16 ≈ Acceleration due to gravity ( ft/ sec ) 2 s = initial drop height (ft)

Solution: = -16 t + 400 h = -16t + s t = ? h = 0 ft s = 400 ft 5 = #Use a Falling Object Model If a penny is drop from the 5th floor of a building which is 400 ft above ground, how long will it take to hit the ground. Solution: 2 = -16 t + 400 2 h = -16t + s –400 –400 1 2 t = ? -400 = -16t -16 -16 h = 0 ft 2 25 = t s = 400 ft 5 = | t | t = 5 seconds ± 5 = t

Assignment Book Pg. 508 – 509 # 34 – 48 all #59, 60