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9.6 β Applications of the
Discriminant
Algebra 1(B)
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Homework Check/Questions
44) ; -3, 545) ; 1, 246) ; 1.73, 9.2753) 4, -254) 4, -155) -2, 3
22 4 30 0x x
2 3 2 0x x 2 11 16 0x x
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Warm UpUse the quadratic formula to solve the following problem:
Mr. V has just autographed a math textbook for the Biebs (aka Justin Bieber). Still in shock over who he has just met, Justin Bieber drops the book. A falcon flying overhead decides he would like to make some money by selling the book on Amazon. If the falcon is 100 feet in the air and dives at a speed of 220 feet per second, how much time does Justin Bieber have to react before the falcon takes the book?
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Warm Up
I canβt believe that just happened. It was Mr. V! OMG!
Autographed Textbook
220 ft/sec
Answer: 0.44 sec
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Objectives:
1. Evaluate the discriminant
2. Use the discriminant to find the number of quadratic solutions
3. Match graphs with their quadratic equations based on the discriminant
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Recall the Quadratic Formulaβ¦
π₯=βπΒ±βπ2β4ππ2π
Discriminant: the expression inside of the radical.
ππβπππ
π2β4ππ
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Using the Discriminant
Discriminant: the expression inside of the radical.π2β4ππ
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PracticeDiscriminant: the expression inside of the radical.π2β4ππ
Use the discriminant to determine how many x-intercepts/solutions/zeros the following quadratic equations have.
one solution
no solution
two solutions
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PracticeDiscriminant: the expression inside of the radical.π2β4ππ
Use the discriminant to determine how many x-intercepts/solutions/zeros the following quadratic equations have. Support your answer up by graphing!
π¦=π₯2β3π₯β4
two solutions
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PracticeDiscriminant: the expression inside of the radical.π2β4ππ
Use the discriminant to determine how many x-intercepts/solutions/zeros the following quadratic equations have. Support your answer up by graphing!
π¦=2 π₯2β2 π₯+3
no solution
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PracticeDiscriminant: the expression inside of the radical.π2β4ππ
Use the discriminant to determine how many x-intercepts/solutions/zeros the following quadratic equations have. Support your answer up by graphing!
π¦=βπ₯2+2 π₯β1
one solution
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MatchingDiscriminant: the expression inside of the radical.π2β4ππ
Use the discriminant to match the equations with their potential graphs!
π¦=π₯2+2π₯+2 π¦=π₯2β4 π₯+4 π¦=β3π₯2+6 π₯β1
A. B. C.
A C B
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Exit Slip Raffleβ’ Complete the three problems below.β’ Exit slips will be collected and random slips will be drawn.β’ If your paper is drawn and you are correct, you must explain your work for the class.β’ Prize: extra credit on tomorrowβs quiz!
Tell if the equation has two solutions, one solution, or no solution.
23 12 12 0x x
22 10 6 0x x
3) Is it possible for the equation below to have a graph like the one shown. EXPLAIN!
2 3 5 0x x1) 2)
One solution No solution
No, because the discriminant of the equation is positive, so the graph
should have two x-intercepts.
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Assignment/Reminder
pg. 544 #9-17
Quiz 9.4-9.6 Monday 4/6!