Problem of the Day Janice is solving the quadratic equation as shown: x2 + 24x – 15 = 0 x2 + 24x – 15 + 15 = 0 + 15 x2 + 24x = 15 Which equation BEST represents the next step Janice would use to solve for x by completing the square? x2 + 24x + 144 = 15 + 144 x2 + 24x + 12 = 15 + 12 x2 + 24x + 48 = 15 + 48 x2 + 24x + 576 = 15 + 576 Problem of the Day

Section 4-6a The Quadratic Formula

Then Now Objectives You solved equations by completing the square. Solve quadratic equations by using the Quadratic Formula.

Common Core State Standards Content Standards N.CN.7 – Solve quadratic equations with real coefficients that have complex solutions. A.SSE.1.b – Interpret complicated expressions by viewing one or more of their parts as a single entity. Mathematical Practices 8) Look for and express regularity in repeated reasoning. Common Core State Standards

Quadratic Formula

Example 1 Two Rational Roots Solve the equation by using the Quadratic Formula: 𝑥 2 +6𝑥=16 Example 1 Two Rational Roots

Example 1 Two Rational Roots Solve the equation by using the Quadratic Formula: 2 𝑥 2 +25𝑥+33=0 Example 1 Two Rational Roots

Example 1 Two Rational Roots Solve the equation by using the Quadratic Formula: 𝑥 2 −8𝑥=33 Example 1 Two Rational Roots

Example 2 One Rational Root Solve the equation by using the Quadratic Formula: 𝑥 2 −16𝑥+64=0 Example 2 One Rational Root

Example 2 One Rational Root Solve the equation by using the Quadratic Formula: 𝑥 2 +34𝑥+289=0 Example 2 One Rational Root

Example 2 One Rational Root Solve the equation by using the Quadratic Formula: −16 𝑥 2 +8𝑥−1=0 Example 2 One Rational Root

Example 3 Irrational Roots Solve the equation by using the Quadratic Formula: 𝑥 2 −8𝑥+9=0 Example 3 Irrational Roots

Example 3 Irrational Roots Solve the equation by using the Quadratic Formula: 3 𝑥 2 +5𝑥+1=0 Example 3 Irrational Roots

Example 3 Irrational Roots Solve the equation by using the Quadratic Formula: 𝑥 2 −6𝑥+2=0 Example 3 Irrational Roots

p.269 #5 – 8, 14, 15, 48 Homework