SWBAT solve quadratic equations Agenda 1 Warmup 15

SWBAT… solve quadratic equations Agenda 1. Warm-up (15 min) 2. Solving quadratic equations (20 min) Warm-Up: Factor each expression: 1. 2. 3. 4. 5. b 2 – 18 b + 32 x 2 + 2 x – 48 n 6 + n 3 – 56 p 2 – 10 pq + 16 q 2 2 b – 25 Mon, 5/23

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: x 2 + 11 x = -18 1. ) x 2 + 11 x + 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 x 2 + 11 x = -18 or x 2 + 11 x = -18 (-2)2 + 11(-2) = -18 (-9)2 + 11(-9) = -18 4 – 22 = -18 81 – 99 = -18 -18 = -18

n n On your graphing calculator graph y = x 2 + 11 x + 18 You might need to change the “window” to: ¨ x-min = -10 ¨ x-max = 10 ¨ x-scale = 1 ¨ y-min = -10 ¨ y-max = 10 ¨ y-scale = 1 n What conclusion can you make about the solutions of a quadratic and it’s graph? n 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. n

n They all mean the same thing!!!

1. 2. What are the roots of x 2 + 2 x = 48? Find all zeros for the function f(x) = x 2 – 3 x – 70

SWBAT… solve quadratic equations Mon, 5/23 Agenda 1. Warm-up (15 min) 2. Review HW 3 / HW 4 (10 min) Warm-Up: 1. A rectangle has an area represented by x 2 – 4 x – 12 feet 2. If the length is x + 2 feet, what is the width of the rectangle? 2. What are the roots of x 2 + 2 x = 48? 3. Find all zeros for the function f(x) = x 2 – 3 x – 70

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 = -16 t 2 + 263 t, 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?