YES! The Quadratic Formula

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Presentation transcript:

YES! The Quadratic Formula Lesson #21 The Quadratic Formula YES! The Quadratic Formula

Recall that 1.The solution when y =0 from factored form y=a(x-z1)(x-z2) 2.The solution when y =0 from standard form y=a(x-h)2 +k When the quadratic function is in General form, y = ax2 +bx + c and cannot be factored easily (answers are square roots) use the…….. QUADRATIC FORMULA

Ex. 1 Case II: 1 zero Case 1. 2 zeros y = x2 + 2x + 1 Find the zeros Case 1. 2 zeros Case II: 1 zero y = 5x2 + 20x - 30 y = x2 + 2x + 1

a a 4a2 2a 4a2 4a2 2a 4a2 2a 2a 2a 2a y = ax2 + bx + c 1. General formula y = a(x2 + bx + c) a 2. Factor out the a y = a(x2 + bx + b2 a 4a2 + c) - b2 3. Make a perfect square trinomial y = a((x + b )2 - b2 + 4a2c) 4. Factor and get a common denominator 2a 4a2 4a2 y = a((x + b )2 - b2 + 4a2c ) 5. Add the numerators 2a 4a2 0 = a(x + b )2 -b2 + 4ac 6. Multiply the a in 2a 4a (x + b )2 = b2 - 4ac 7. Move term to other side of equal sign and divide by a 2a 4a2 (x + b ) = b2 - 4ac 8. –b/2a on both sides 2a 4a x = -b b2 - 4ac 9. Final formula 2a

Homework Handout #1-15