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

2. REVIEW: Compare the different ways to solve the following quadratic equations.
𝑥 2 −11𝑥+30= 𝑥 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= 𝑥−1=0 30 −7 −𝟓 −𝟔
−11
𝑥−5 𝑥−6 =0
𝑥−5= 𝑥−6=0
3𝑥=2
𝒙= 𝟐 𝟑
𝒙=𝟏
𝒙=𝟓
𝒙=𝟔

3. Quadratic Formula Rap

4. 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

5. SOLVING QUADRATICS BY THE QUADRATIC FORMULA
EXAMPLE: Solve the following quadratics.
1. 𝑥 2 +3𝑥−2= 𝑥 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±
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

6. SOLVING QUADRATICS BY THE QUADRATIC FORMULA
EXAMPLE: Solve the following quadratics.
1. −𝑥 2 +4𝑥−5= −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= − −2
𝑥= −4− 11 −2
𝒙=𝟏
𝒙=𝟐− 𝟏𝟏 𝟐
𝒙=𝟐+ 𝟏𝟏 𝟐

7. 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