SWBAT solve quadratic equations in the form ax

SWBAT… solve quadratic equations in the form ax 2 + bx + c Tues, 5/14 Agenda 1. Warm-up (10 min) 2. Review HW#1 and HW#2 (20 min) 3. ax 2 + bx + c = 0 (20 min) Warm-Up: 1. 2. 4 27 y z 3 6 18 y z + 2 Solve: x – 18 = -11 x HW#3: Solving quadratic equations: ax 2 + bx + c = 0

Directions: Use the distributive property to factor each polynomial. 1. 27 y 4 z + 18 y 3 z 6 Step 1. Take out GCF 9 y 3 z (3 y) + 9(2 z 5) Step 2. Rewrite each term using the GCF 9 y 3 z(3 y + 2 z 5) Step 3. Distributive Property

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 = 0 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 = 0 or x 2 + 11 x – 18 = 0 (-2)2 + 11(-2) – 18 = (-9)2 + 11(-9) – 18 = 0 4 – 22 – 18 = 0 81 – 99 – 18 = 0 -18 – 18 = 0

n On your graphing calculator graph x 2 + 11 x + 18 n You will need to change the “window” ¨ x-min = -15 ¨ y-max = 15 ¨ y-min = -15 ¨ y-max = 15 n 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. Therefore, the solutions of a quadratic equation are where the parabola crosses the x-axis.

Solving Quadratic Equations: ax 2 + bx + c = 0 Ex 1: Find all zeros for the function f(x) = 2 x 2 – 6 x – 8 n Always look for a GCF of a polynomial before you factor.

Factoring Trinomials: ax 2 + bx + c Ex 2: Solve for x: 3 x 2 – 10 x + 7 = 0.

Ex 3: Solve: 2 x 2 – 5 x – 12 = 0

Ex 4: Solve: 4 x 2 – 12 x + 5 = 0

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?

Vertical Motion Model A model for the vertical motion of a projected object is given by h = -16 t 2 + vt + ho h is the height in feet t is the time in seconds v is the initial velocity in feet per second ho is the initial height in feet

Ken throws the discus at a school meet. The equation h = -16 t 2 + 95 t + 6 models the throw. a. What is the initial height of the discus? b. What is the initial velocity of the discus? c. After how many seconds does the discus hit the ground? h = -16 t 2 + vt + ho