SWBAT solve quadratic equations Wed 413 Agenda 1
SWBAT… solve quadratic equations Wed 4/13 Agenda 1. Warm-up (15 min) 2. Review hw#3 (10 min) 3. Solving quadratic equations (20 min) 4. Work on hw#4 (15 min) Warm-Up: Factor each expression and check: 1. 2. 3. a 2 – 3 a – 18 p 2 – 10 pq + 16 q 2 n 6 + n 3 – 56 HW#4: Quadratic Equations: x 2 + bx + c
To solve quadratic equations: 1. ) Set equation = 0 2. ) Factor the equation 3. ) Set each factor = 0 4. ) Solve each variable 5. ) Check both solutions 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: Plug both answers into 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 x 2 + 11 x + 18 You will need to change the “window” ¨ x-min = -15 ¨ y-max = 15 ¨ y-min = -15 ¨ y-max = 15 n n What conclusion can you make about the solutions of a quadratic and it’s graph? The solutions of a quadratic may also be called roots, zeros or x-intercepts.
Warm-Up: Solve each equation: 1. 2. 3. 4. -42 – m + m 2 = 0 c 2 = 3 c Find all the values of k: x 2 + kx – 19 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?
Real-life 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?
- Slides: 6