Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1...
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Transcript of Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1...
![Page 1: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/1.jpg)
Objective:Solving Quadratic Equations by Finding Square Roots
This lesson comes from chapter 9.1 from your
textbook, page 503
![Page 2: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/2.jpg)
Quadratic Equations
Standard form: ax2 + bx + c = 0
![Page 3: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/3.jpg)
Find the square root of numbersππ=ΒΏππβππ=ΒΏπ
ββππ=ΒΏ βπ
βπ=ΒΏπββπ=ΒΏπ πππ πππ ππππππ
![Page 4: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/4.jpg)
Find the square root of numbers
βππβππ=ΒΏβππ=π
ββππ+π=ΒΏββπ=βπ
1.
2.
![Page 5: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/5.jpg)
Find the square root of numbers
βπ (π )+ππ=ΒΏβππ=π
βπΒΏΒΏ
1.
2. βππ=π
![Page 6: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/6.jpg)
Find the square root of numbersππ=π
π=Β±π
βππ=βπ
1.
![Page 7: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/7.jpg)
Key ConceptsWhen x2 = d
If d > 0, then x2 = d has two solutions
example:
If d = 0, then x2 = d has one solution
example:
If d < 0, then x2 = d has no real solution
example:
ππ=πππ
ππ=βπ
ππ=π
![Page 8: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/8.jpg)
Find the square root of numbers1. 2. ππ=ππ
π=Β±π
βππ=βππππ=π
π=π
βππ=βπ
![Page 9: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/9.jpg)
Find the square root of numbers1. 2. ππ+π=ππ
π=Β±π
βππ=βππ
βπβπππ=ππ
ππβπ=ππ
π=Β±π
βππ=βππ
+π+πππ=ππ
![Page 10: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/10.jpg)
Find the square root of numbers1. 2. πππ=ππ
π=Β±π
βππ=βππ
ππππ=ππ
πππβπ=ππ
βππ=βππ
ππππ=ππ
+π+ππππ=ππ
π=Β±π
![Page 11: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/11.jpg)
Find the square root of numbers1. 2. πππ+π=ππ
π=Β±πβππ=βππ
ππππ=ππ
βπβππππ=ππ
π ππ+π=ππ
π=Β±π
βππ=βππ
ππππ=ππ
βπβππ ππ=ππ
![Page 12: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/12.jpg)
Real Life: Equation of a falling object
When an object is dropped, the speed with which it falls continues to increase. Ignoring air resistance, its height h can be approximated by the falling object model.
sth 216h is the ending height in feet above the groundt is the number of seconds the object has been fallings is the starting height from which the object was dropped
![Page 13: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/13.jpg)
Application
Sarah is going to drop a water balloon from a height of 144 feet. To the nearest tenth of a second, about how long will it take for the balloon to hit the ground? Assume there is no air resistance.
![Page 14: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/14.jpg)
The question asks to find the time it takes for the container to hit the ground.
Initial height (s) = 144 feet
Height when its ground (h) = 0 feet
Time it takes to hit ground (t) = unknown
sth 216
![Page 15: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/15.jpg)
Substitutesth 216
π=βππππ+πππ
3 sec.
βπ=βππ
βππβππ
βπππβπππβπππ=βππππ
π=ππ
![Page 16: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/16.jpg)
Substitutesth 216
π=βππππ+πππ
4.24 sec.
βππ=βππ
βππβππ
βπππβπππβπππ=βππππ
ππ=ππ
![Page 17: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/17.jpg)
Find the square root of numbers1. 2. πππβπ=π
π=Β±πβππ=βπ
ππππ=π
+π+ππππ=π
πππ+π=ππβπβππππ=ππππππ=πβππ=βπ
π=Β±π
![Page 18: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/18.jpg)
Application
An engineering student is in an βegg dropping contest.β The goal is to create a container for an egg so it can be dropped from a height of 32 feet without breaking the egg. To the nearest tenth of a second, about how long will it take for the eggβs container to hit the ground? Assume there is no air resistance.
![Page 19: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/19.jpg)
The question asks to find the time it takes for the container to hit the ground.
Initial height (s) = 32 feet
Height when its ground (h) = 0 feet
Time it takes to hit ground (t) = unknown
sth 216
![Page 20: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/20.jpg)
Substitutesth 216
π=βππππ+ππ
Approximately 1.4 sec.
βπ=βππ
βππβππ
βππβππβππ=βππππ
π=ππ
![Page 21: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/21.jpg)
Evaluate a Radical Expression
βππβπππ=β(βπ)πβπ(π)(βπ)=βπβπ(βπ)
βπ+ππ=βππ=π
![Page 22: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/22.jpg)
Perfect Squares: Numbers whose square roots are integers or quotients of integers.
1316912144
1112110100
981864749
636525416
392411
![Page 23: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/23.jpg)
What is a square root?
If a number square (b2) = another number (a), then b is the square root of a.
Example: If 32 = 9, then 3 is the square root of 9
![Page 24: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/24.jpg)
Quadratic Equations
Standard form: ax2 + bx + c = 0a is the leading coefficient and cannot be equal to zero.If the value of b were equal to zero, the equation becomes ax2 + c = 0.We can solve equations is this form by taking the square root of both sides.
![Page 25: Objective: Solving Quadratic Equations by Finding Square Roots This lesson comes from chapter 9.1 from your textbook, page 503.](https://reader036.fdocuments.net/reader036/viewer/2022062720/56649f045503460f94c181af/html5/thumbnails/25.jpg)
Some basicsβ¦
All positive numbers have two square rootsThe 1st is a positive square root, or principal square root.The 2nd is a negative square rootSquare roots are written with a radical symbol You can show both square roots by using the βplus-minusβ symbol Β±