TODAY IN GEOMETRY… Review methods for solving quadratic equations Learning Goal: You will solve quadratics by using the Quadratic Formula In Class Practice

REVIEW: Compare the different ways to solve the following quadratic equations. 𝑥 2 −11𝑥+30=0 6𝑥 2 −7𝑥+2=0 2. Coefficient greater than 1 1. Coefficient of 1 ∗ + 12 ∗ + −𝟑 −𝟒 6 𝑥 2 −3𝑥−4𝑥+2=0 6 𝑥 2 −3𝑥 −4𝑥+2 =0 3𝑥 𝑥−1 −2 𝑥−1 =0 3𝑥−2 𝑥−1 =0 3𝑥−2=0 𝑥−1=0 30 −7 −𝟓 −𝟔 −11 𝑥−5 𝑥−6 =0 𝑥−5=0 𝑥−6=0 + 2 + 2 3𝑥=2 3 3 𝒙= 𝟐 𝟑 + 1 + 1 𝒙=𝟏 + 5 + 5 𝒙=𝟓 + 6 + 6 𝒙=𝟔

Quadratic Formula Rap

SOLVING QUADRATICS BY THE QUADRATIC FORMULA If we cannot solve by factoring we can find the zeros by using the QUADRATIC FORMULA: If 𝑎𝑥 2 +𝑏𝑥+𝑐=0 then 𝒙= −𝒃± 𝒃 𝟐 −𝟒𝒂𝒄 𝟐𝒂

SOLVING QUADRATICS BY THE QUADRATIC FORMULA EXAMPLE: Solve the following quadratics. 1. 𝑥 2 +3𝑥−2=0 2. 4𝑥 2 −12𝑥+9=0 𝑎 𝑏 𝑐 𝑎 𝑏 𝑐 1 𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎 𝑥= −(3)± (3) 2 −4(1)(−2) 2(1) 𝑥= −3± 9−(−8) 2 𝑥= −3± 17 2 𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎 𝑥= −(−12)± (−12) 2 −4(4)(9) 2(1) 𝑥= 12± 144−144 2 𝑥= 12± 0 2 𝒙=𝟔 𝒙= −𝟑+ 𝟏𝟕 𝟐 𝒙= −𝟑− 𝟏𝟕 𝟐

SOLVING QUADRATICS BY THE QUADRATIC FORMULA EXAMPLE: Solve the following quadratics. 1. −𝑥 2 +4𝑥−5=0 2. −5𝑥 2 +10𝑥−5=0 𝑎 𝑏 𝑐 𝑎 𝑏 𝑐 1 𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎 𝑥= −(4)± (4) 2 −4(−1)(−5) 2(−1) 𝑥= −4± 16−(5) −2 𝑥= −4± 11 −2 𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎 𝑥= −(10)± (10) 2 −4(−5)(−5) 2(−5) 𝑥= −10± 100−100 −10 𝑥= −10± 0 −10 𝑥= −4+ 11 −2 𝑥= −4− 11 −2 𝒙=𝟏 𝒙=𝟐− 𝟏𝟏 𝟐 𝒙=𝟐+ 𝟏𝟏 𝟐

Solving Quadratics by Quadratic Formula WS IN CLASS WORK #5: Solving Quadratics by Quadratic Formula WS Previous Assignments: HW#1: Substitution and Elimination WS HW#2: Factor Binomials and Trinomials WS HW#3: Factor Trinomials with coeff. greater than 1 WS HW#4: Solving Quadratics by Factoring WS