Solve x2 + 2x + 24 = 0 by completing the square. Warmup Solve x2 + 2x + 24 = 0 by completing the square. A. –12, 12 B. –2, 2 C. D.

4-6 The Quadratic Formula and the Discriminant Goal: Solve quadratic equations by using the Quadratic Formula. Use the discriminant to determine the number and type of roots of a quadratic equation.

15. Solve the equation by using the Quadratic Formula. 4 𝑥 2 −6=−12𝑥 4x2 + 12x − 6 = 0 a = 4, b = 12, c = -6 𝑥= −𝑏 ± 𝑏 2 −4𝑎𝑐 2𝑎 𝑥= −12 ± (12) 2 −4 4 (−6) 2(4) 𝑥= −12 ± 144+96 8 𝑥= −12 ± 240 8 𝑥= −12 ±4 15 8 𝑥= −3 ± 15 2

The discriminant: 𝑏 2 −4𝑎𝑐; the value under the radical in the quadratic formula. It helps you decide (discriminate between) how many solutions and what kind of solutions they will be.

KEY CONCEPT: DISCRIMINANT Consider 𝑎 𝑥 2 +𝑏𝑥+𝑐=0, 𝑎≠0 Value of discriminant Type and Number of Roots Example of Graph of Related Function 𝑏 2 −4𝑎𝑐>0 2 real roots 𝑏 2 −4𝑎𝑐=0 1 real root 𝑏 2 −4𝑎𝑐<0 2 complex roots

Complete parts a-c for the quadratic equation. Find the value of the discriminant Describe the number and type of roots Find the EXACT solutions by using the quadratic formula 23. 6 𝑥 2 +5𝑥−1=0 End of Notes

Find a partner. Your partnership needs: A bag of colored cards. A calculator for each of you. Scratch paper for each of you. A form to record answers on for each of you. Turn desks to face each other. Make a matching set of 3 cards consisting of beginning quadratic equation, filled in quadratic formula, and final simplified answers. Check with either Emma or I.

Since you did this activity in class, you do not have to do any of the rest of the homework for Section 4-6. Instead, your recorded matches will be your work, along with your scratch paper. Exit Game at kahoot.it