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9.5 Quadratic Formula.

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Presentation on theme: "9.5 Quadratic Formula."β€” Presentation transcript:

1 9.5 Quadratic Formula

2 What We Will Learn Solve using Quadratic Formula
Interpret discriminant Choose methods for solving quadratics

3 Essential Question How can you use the appropriate method to solve quadratic equations?

4 Needed Vocab Quadratic Formula: π‘₯= βˆ’π‘Β± 𝑏 2 βˆ’4π‘Žπ‘ 2π‘Ž
Discriminant: 𝑏 2 βˆ’4π‘Žπ‘

5 Ex. 1 Using Quadratic Formula
Solve 2π‘₯ 2 βˆ’5π‘₯+3=0 π‘Ž=2, 𝑏=βˆ’5, 𝑐=3 π‘₯= 5Β± (βˆ’5) 2 βˆ’4(2)(3) 2(2) π‘₯= 5Β± 25βˆ’24 4 π‘₯= 5Β± 1 4 π‘₯= , π‘₯= 5βˆ’1 4 π‘₯= 3 2 , π‘₯=1 Steps 1. get = to 0 2. plug in a, b, c 3. do pemdas

6 Ex. 1 Cont. Solve βˆ’3π‘₯ 2 +2π‘₯+7=0 π‘Ž=βˆ’3, 𝑏=2, 𝑐=7
π‘₯= βˆ’2Β± βˆ’4(βˆ’3)(7) 2(βˆ’3) π‘₯= βˆ’2Β± βˆ’6 π‘₯= βˆ’2Β± 88 βˆ’6 π‘₯= βˆ’ βˆ’6 , π‘₯= βˆ’2βˆ’ 88 βˆ’6 π‘₯=βˆ’1.23, π‘₯=1.90 Your Practice Solve 2π‘₯ 2 +9π‘₯+7=3 βˆ’3 βˆ’3 2π‘₯ 2 +9π‘₯+4=0 π‘Ž=2, 𝑏=9, 𝑐=4 π‘₯= βˆ’9Β± βˆ’4(2)(4) 2(2) π‘₯= βˆ’9Β± 81βˆ’32 4 π‘₯= βˆ’9Β± π‘₯= βˆ’9+7 4 , π‘₯= βˆ’9βˆ’7 4 π‘₯=βˆ’ 1 2 , π‘₯=βˆ’4

7 Exs. 3/4 Finding Number of Real Solutions and Number of x-intercepts
Use discriminant 𝑏 2 βˆ’4π‘Žπ‘ If 𝑏 2 βˆ’4π‘Žπ‘>0, then If 𝑏 2 βˆ’4π‘Žπ‘=0, then If 𝑏 2 βˆ’4π‘Žπ‘<0, then 2 real solutions one real solution no real solutions 2 intercepts one intercept no intercepts

8 Exs. 3/4 cont. Determine number of real solutions and x-intercepts of:
π‘₯ 2 +8π‘₯βˆ’3=0 π‘Ž=1, 𝑏=8, 𝑐=βˆ’3 8 2 βˆ’4 1 βˆ’3 64+12 76 Two solutions and two intercepts Steps 1. get = to 0 2. use discriminant 𝑏 2 βˆ’4π‘Žπ‘ 3. simplify

9 Exs. 3/4 cont. Determine number of solutions and x-intercepts of:
9π‘₯ 2 +1=6π‘₯ βˆ’6π‘₯ βˆ’6π‘₯ 9π‘₯ 2 βˆ’6π‘₯+1=0 π‘Ž=9, 𝑏=βˆ’6, 𝑐=1 (βˆ’6) 2 βˆ’4 9 1 36βˆ’36 One solution and one x-int Determine number or solutions and x-intercepts of: 𝑦= 2π‘₯ 2 +3π‘₯+9 π‘Ž=2, 𝑏=3, 𝑐=9 3 2 βˆ’4(2)(9) 9βˆ’72 -68 No solution and no x-int

10 Ex. 5 Choosing Any Method Method When to Use Factoring
Easily factored, π‘₯ 2 +𝑏π‘₯+𝑐 Square Roots π‘₯ 2 βˆ’π‘‘=0 Complete the Square π‘Žπ‘₯ 2 +𝑏π‘₯+𝑐 when a is one and b is even Quadratic Formula Anytime! Always Works!! π‘₯= βˆ’π‘Β± 𝑏 2 βˆ’4π‘Žπ‘ 2π‘Ž


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