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9.5 Quadratic Formula
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What We Will Learn Solve using Quadratic Formula
Interpret discriminant Choose methods for solving quadratics
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Essential Question How can you use the appropriate method to solve quadratic equations?
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Needed Vocab Quadratic Formula: π₯= βπΒ± π 2 β4ππ 2π
Discriminant: π 2 β4ππ
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Ex. 1 Using Quadratic Formula
Solve 2π₯ 2 β5π₯+3=0 π=2, π=β5, π=3 π₯= 5Β± (β5) 2 β4(2)(3) 2(2) π₯= 5Β± 25β24 4 π₯= 5Β± 1 4 π₯= , π₯= 5β1 4 π₯= 3 2 , π₯=1 Steps 1. get = to 0 2. plug in a, b, c 3. do pemdas
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Ex. 1 Cont. Solve β3π₯ 2 +2π₯+7=0 π=β3, π=2, π=7
π₯= β2Β± β4(β3)(7) 2(β3) π₯= β2Β± β6 π₯= β2Β± 88 β6 π₯= β β6 , π₯= β2β 88 β6 π₯=β1.23, π₯=1.90 Your Practice Solve 2π₯ 2 +9π₯+7=3 β3 β3 2π₯ 2 +9π₯+4=0 π=2, π=9, π=4 π₯= β9Β± β4(2)(4) 2(2) π₯= β9Β± 81β32 4 π₯= β9Β± π₯= β9+7 4 , π₯= β9β7 4 π₯=β 1 2 , π₯=β4
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Exs. 3/4 Finding Number of Real Solutions and Number of x-intercepts
Use discriminant π 2 β4ππ If π 2 β4ππ>0, then If π 2 β4ππ=0, then If π 2 β4ππ<0, then 2 real solutions one real solution no real solutions 2 intercepts one intercept no intercepts
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Exs. 3/4 cont. Determine number of real solutions and x-intercepts of:
π₯ 2 +8π₯β3=0 π=1, π=8, π=β3 8 2 β4 1 β3 64+12 76 Two solutions and two intercepts Steps 1. get = to 0 2. use discriminant π 2 β4ππ 3. simplify
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Exs. 3/4 cont. Determine number of solutions and x-intercepts of:
9π₯ 2 +1=6π₯ β6π₯ β6π₯ 9π₯ 2 β6π₯+1=0 π=9, π=β6, π=1 (β6) 2 β4 9 1 36β36 One solution and one x-int Determine number or solutions and x-intercepts of: π¦= 2π₯ 2 +3π₯+9 π=2, π=3, π=9 3 2 β4(2)(9) 9β72 -68 No solution and no x-int
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Ex. 5 Choosing Any Method Method When to Use Factoring
Easily factored, π₯ 2 +ππ₯+π Square Roots π₯ 2 βπ=0 Complete the Square ππ₯ 2 +ππ₯+π when a is one and b is even Quadratic Formula Anytime! Always Works!! π₯= βπΒ± π 2 β4ππ 2π
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