Aim: What is the quadratic formula and how do we use it?

1. Aim: What is the quadratic formula and how do we use it? Solve by completing the square: x2 + 2x – 12 = 0 Do Now:

2. x = -5 x = 2 Solving Quadratics by Graphing Find the zeros by graphing: x2 + 3x – 10 = 0

3. Solve: x2 + 3x – 10 = 0 x = -5 x = 2 Solving Quadratics by Factoring (x + 5)(x – 2) =0 (x + 5) = 0 (x - 2) = 0 x = -5 x = 2 Graph the equation y = x2 + 3x – 10 on calculator the roots of the quadratic - where the parabola crosses the x-axis.

4. Solving Quadratics Graph: x2 – 10x + 13 = y not factorable roots of this quadratic are notsweet! How do we determine what the roots of this and similar quadratic equations are? Quadratic Formula

5. quadratic in standard form Solving Quadratics using the Formula y = ax2 + bx + c Quadratic Formula • - two answers to quadratic one added to -b second subtracted from -b b2 – 4ac - discriminant the expression under the radical sign

6. Quadratic Formula Solving Quadratics using the Formula y = ax2 + bx + c Solve: x2 – 10x + 13 = 0 a = 1 b = -10 c = 13

7. x2 – 10x + 13 = 0 Check your answer 25 + 12 – 50 + 13 = 0 0 = 0 check 2nd value of x also

8. Model Problems Find the roots of each equation by using the quadratic formula. Express irrational roots in simplest radical form. {-6, 4} x2 + 2x – 24 = 0 2x2 + 5 = 11x {1/2, 5} x2 + 4x = 16 Express to nearest hundredth 4x2 = 4x + 39 {-2.66, 3.66}

9. A = lw Model Problems The length of a rectangle is 4 more than its width. Find its dimensions if its area is 8. x = width x + 4 = length x(x + 4) = 8 x2 + 4x = 8 Unfactorable x2 + 4x – 8 = 0 a = 1, b = 4, c = -8

10. 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 = width x + 4 = length x(x + 4) = 8 x2 + 4x – 8 = 0 width: negative answer not possible length = x + 4

11. Aim: What is the quadratic formula and how do we use it? Solve by graphing using quadratic formula factoring 2x2 = x + 15 Do Now: