&rpsohwlqj wkh 6txduh...microsoft powerpoint - 9.4 notes author: scott stuhlman created date:...
TRANSCRIPT
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Solving Quadratic Equations by Completing the SquareSection 9.4
Group DiscussionWhich of the following are perfect square trinomials?
Group Discussion
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Group DiscussionCan you fill in the blank to make each expression a perfect square trinomial?
Group Discussion
Completing the SquareCompleting the SquareThe Process:1. Find half of (the coefficient of )2. Square the result from Step 13. Add the result from Step 2 to the end of +
Notes and VocabNotes and Vocab
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Completing the SquareCompleting the SquareEXAMPLE 1Find the value of that makes + 4 + a perfect square trinomial.
Guided PracticeGuided Practice
Completing the SquareCompleting the SquareEXAMPLE 2Find the value of that makes − 8 + a perfect square trinomial.
Guided PracticeGuided Practice
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Completing the SquareCompleting the SquareEXAMPLE 3Find the value of that makes − 12 + a perfect square trinomial.
Individual PracticeIndividual Practice
Completing the SquareCompleting the SquareEXAMPLE 4Find the value of that makes + 26 + a perfect square trinomial.
Individual PracticeIndividual Practice
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Solving Equations in Factored FormSolving Equations in Factored FormEXAMPLE 1 + 5 = 49
Guided PracticeGuided Practice
Solving Equations in Factored FormSolving Equations in Factored FormEXAMPLE 2 − 3 = 100
Guided PracticeGuided Practice
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Solving Equations in Factored FormSolving Equations in Factored FormEXAMPLE 3− 1 = 9 EXAMPLE 4+ 2 = 1
Individual PracticeIndividual Practice
Group DiscussionWhat you know:
+ 6 + 9 is a perfect square trinomialWhat you have known in the past:
+ 6 + 9 = + 3
How do you think you could solve for ?+ 6 + 9 = 16
Group Discussion
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Solving Equations by Completing the SquareSolving Equations by Completing the SquareThe Process:1. Get + by itself on one side of the equal sign2. Complete the square for +3. Factor the left side to be a binomial squared4. Take the square root of both sides5. Solve for
Notes and VocabNotes and Vocab
Solving Equations by Completing the SquareSolving Equations by Completing the SquareEXAMPLE 1 − 6 + 12 = 19
Guided PracticeGuided Practice
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Solving Equations by Completing the SquareSolving Equations by Completing the SquareEXAMPLE 2 − 14 + 5 = −28
Guided PracticeGuided Practice
Solving Equations in Factored FormSolving Equations in Factored FormEXAMPLE 3− 8 − 1 = 8 EXAMPLE 4+ 6 − 10 = 6
Individual PracticeIndividual Practice
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Group Challenge!Group Challenge!Solve for by completing the square.
−2 + 8 + 18 = 0
Group Challenge!Group Challenge!
Group DiscussionWhat you know:
+ 6 + 9 = + 3What you have known in the past:
= + 3 − 5 is in vertex form.
How do you think you could write this equation in vertex form?= + 8 − 2
Group Discussion
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Converting Standard Form to Vertex FormConverting Standard Form to Vertex FormThe Process:1. Change to a 02. Bring the constant term to the other side of the equation3. Complete the square as usual4. Bring the constant term back over5. Replace the 0 with
Notes and VocabNotes and Vocab
Converting Standard Form to Vertex FormConverting Standard Form to Vertex FormEXAMPLE 1 = + 6 + 4
Guided PracticeGuided Practice
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Converting Standard Form to Vertex FormConverting Standard Form to Vertex FormEXAMPLE 2 = − 16 + 57
Guided PracticeGuided Practice
Converting Standard Form to Vertex FormConverting Standard Form to Vertex FormEXAMPLE 3= − 10 + 23 EXAMPLE 4= + 4 − 1
Individual PracticeIndividual Practice
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Group Challenge!Group Challenge!Convert the equation to vertex form.
= + 3 − 1
Group Challenge!Group Challenge!