2. Aim: Quadratic Formula Course: Adv. Alg. & Trig. Aim: What is the quadratic formula and how do we use it? Do Now: Solve by completing the square: x 2 + 2x – 12 = 0

3. Aim: Quadratic Formula Course: Adv. Alg. & Trig. Solving Quadratics by Graphing Find the zeros by graphing: x 2 + 3x – 10 = 0 x = -5 x = 2

4. Aim: Quadratic Formula Course: Adv. Alg. & Trig. Solving Quadratics by Factoring Solve: x 2 + 3x – 10 = 0 (x + 5)(x – 2) = 0 (x + 5) = 0(x - 2) = 0 x = -5x = 2 Graph the equation y = x 2 + 3x – 10 on calculator x = -5 x = 2 the roots of the quadratic - where the parabola crosses the x-axis.

5. Aim: Quadratic Formula Course: Adv. Alg. & Trig. Solving Quadratics Graph: x 2 – 10x + 13 = y roots of this quadratic are not sweet! not factorable How do we determine what the roots of this and similar quadratic equations are? Quadratic Formula

6. Aim: Quadratic Formula Course: Adv. Alg. & Trig. b 2 – 4ac - discriminant the expression under the radical sign Solving Quadratics using the Formula Quadratic Formula  - two answers to quadratic one added to -b second subtracted from -b y = ax 2 + bx + c quadratic in standard form

7. Aim: Quadratic Formula Course: Adv. Alg. & Trig. Solving Quadratics using the Formula Quadratic Formula Solve: x 2 – 10x + 13 = 0 a = 1 b = -10 c = 13 y = ax 2 + bx + c

8. Aim: Quadratic Formula Course: Adv. Alg. & Trig. Check your answer x 2 – 10x + 13 = 0 25 + 12 – 50 + 13 = 0 0 = 0 check 2nd value of x also

9. Aim: Quadratic Formula Course: Adv. Alg. & Trig. Model Problems x 2 + 2x – 24 = 0 Find the roots of each equation by using the quadratic formula. Express irrational roots in simplest radical form. 2x 2 + 5 = 11x 4x 2 = 4x + 39 Express to nearest hundredth {-6, 4} {1/2, 5} x 2 + 4x = 16 {-2.66, 3.66}

10. Aim: Quadratic Formula Course: Adv. Alg. & Trig. A = lw Model Problems The length of a rectangle is 4 more than its width. Find its dimensions if its area is 8. x = widthx + 4 = length x(x + 4) = 8 x 2 + 4x = 8 x 2 + 4x – 8 = 0Unfactorable a = 1, b = 4, c = -8

11. Aim: Quadratic Formula Course: Adv. Alg. & Trig. A = lw Model Problems (con’t) The length of a rectangle is 4 more than its width. Find its dimensions if its area is 8. x = widthx + 4 = length negative answer not possible width: length = x + 4 x(x + 4) = 8x 2 + 4x – 8 = 0

12. Aim: Quadratic Formula Course: Adv. Alg. & Trig. Aim: What is the quadratic formula and how do we use it? Do Now: Solve by graphing using quadratic formula factoring 2x 2 = x + 15