SWBAT… solve quadratic equations Mon, 5/21 Agenda Warm-up (15 min) Solving quadratic equations (20 min) Warm-Up: Factor: b2 – 18b + 32 Factor: x2 + 2x – 48 Take out HW#1 and HW#2 – Investigation Factoring 4 problems from agenda and HW#1 and HW#2 (b – 2)(b – 16) (x – 6)(x + 8)

Solving quadratic equations: 1.) Set equation = 0 2.) Factor the equation 3.) Set each factor = 0 4.) Solve for each equation 5.) Check both solutions by plugging into the original equation Example: x2 + 11x = -18 1.) x2 + 11x + 18 = 0 2.) (x + 2)(x + 9) = 0 3.) x + 2 = 0 or x + 9 = 0 4.) x = -2 or x = -9

CHECK both answers separately by plugging each answer into the original equation x2 + 11x = -18 or x2 + 11x = -18 (-2)2 + 11(-2) = -18 (-9)2 + 11(-9) = -18 4 – 22 = -18 81 – 99 = -18 -18 = -18 -18 = -18

What conclusion can you make about the solutions of a quadratic and it’s graph? Conclusion: The solutions of a quadratic are where the parabola crosses the x-axis. The solutions of a quadratic may also be called roots, zeros or x-intercepts.

SWBAT… solve quadratic equations Mon, 5/23 Agenda Warm-up (20 min) Solving quadratic equations (20 min) Warm-Up: A rectangle has an area represented by x2 – 4x – 12 feet2. If the length is x + 2 feet, what is the width of the rectangle? Factor: n6 + n3 – 56 Factor: p2 – 10pq + 16q2 What are the roots of x2 + 2x = 48? (x – 6) (n3 – 7)(n3 + 8) (p – 2q)(p – 8q) x = 6 or -8

x = -8 or x = 6 Sketch what the graph of y = x2 + 2x – 48 would look like. x = -8 or x = 6

Firework Example: A ten-inch firework shell is fired from ground level. The height of the shell in feet upon being fired is modeled by the formula h = -16t2 + 263t, where t is the time in seconds from being launched. a.) Write the expression that represents the height in factored form. b.) At what time will the height be 0? Is this answer practical? Explain. c.) What is the height of the shell 8 seconds and 10 seconds after being fired? d.) At 10 seconds, what do we know about the shell’s path? t(-16t + 263) 0 and 16.4375 seconds. Yes, the shell starts at ground level and is in the air for 16.4375 seconds before landing on the ground again. 1080 ft, 1030 ft The shell has begun to fall

SWBAT… solve quadratic equations Thurs, 5/23 Agenda Warm-up (20 min) Solving quadratic equations (20 min) Warm-Up: A rectangle has an area represented by x2 – 18x + 32 feet2. If the width is x – 16 feet, what is the length of the rectangle? Find all zeros of the function f(x) = x2 − 3x – 10. Explain how the solutions can be obtained from the graph? x – 2

What are the solutions?

x2 + kx – 19 (x –19)(x + 1) or (x + 19)(x – 1) k = -18 k = 18 Find all values of k so that each polynomial can be factored using integers x2 + kx – 19 (x –19)(x + 1) or (x + 19)(x – 1) k = -18 k = 18

x2 + kx + 14 (x – 2)(x – 7) (x + 2)(x + 7) k = -9 k = 9 Find all values of k so that each polynomial can be factored using integers x2 + kx + 14 (x – 2)(x – 7) (x + 2)(x + 7) k = -9 k = 9 (x – 14)(x – 1) (x + 1)(x + 14) k = -15 k = 15