Warm Up. Solving Quadratic Equations by the Quadratic Formula.
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Transcript of Warm Up. Solving Quadratic Equations by the Quadratic Formula.
![Page 1: Warm Up. Solving Quadratic Equations by the Quadratic Formula.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f165503460f94c2b737/html5/thumbnails/1.jpg)
Warm Up
𝐹𝑜𝑖𝑙(𝑥+3)(2 𝑥+2)
![Page 2: Warm Up. Solving Quadratic Equations by the Quadratic Formula.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f165503460f94c2b737/html5/thumbnails/2.jpg)
Solving Quadratic Equations by the
Quadratic Formula
![Page 3: Warm Up. Solving Quadratic Equations by the Quadratic Formula.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f165503460f94c2b737/html5/thumbnails/3.jpg)
Refresh
• Remember the GENERAL FORM of a quadratic equation is
Where a,b and c are numbers.
![Page 4: Warm Up. Solving Quadratic Equations by the Quadratic Formula.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f165503460f94c2b737/html5/thumbnails/4.jpg)
Practice
• Write in general form and identify a,b and c.
• We need to add 3 to both sides
• a= 1 b= -5 c= 3
![Page 5: Warm Up. Solving Quadratic Equations by the Quadratic Formula.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f165503460f94c2b737/html5/thumbnails/5.jpg)
You try
• Answer:
• a=3 b= -4 c=5
![Page 6: Warm Up. Solving Quadratic Equations by the Quadratic Formula.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f165503460f94c2b737/html5/thumbnails/6.jpg)
Try again: put in general form
• Answer:
• a=1 b=0 c= -10
![Page 7: Warm Up. Solving Quadratic Equations by the Quadratic Formula.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f165503460f94c2b737/html5/thumbnails/7.jpg)
What does it mean to “solve”?
• When you are asked to “solve” a quadratic, it is asking you to find the roots.
![Page 8: Warm Up. Solving Quadratic Equations by the Quadratic Formula.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f165503460f94c2b737/html5/thumbnails/8.jpg)
THE QUADRATIC FORMULA
2 4
2
b b acx
a
![Page 9: Warm Up. Solving Quadratic Equations by the Quadratic Formula.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f165503460f94c2b737/html5/thumbnails/9.jpg)
What do we do with it?
Step 1: Put in General form, and set equation = to 0.
Step 2: Identify a, b, and c in your quadratic .
Step 3: Substitute a.b and c into the quadratic formula.
![Page 10: Warm Up. Solving Quadratic Equations by the Quadratic Formula.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f165503460f94c2b737/html5/thumbnails/10.jpg)
Example
• a=1. b=4. c=3
![Page 11: Warm Up. Solving Quadratic Equations by the Quadratic Formula.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f165503460f94c2b737/html5/thumbnails/11.jpg)
Example 1 continued
• x=-1 and x=-3
![Page 12: Warm Up. Solving Quadratic Equations by the Quadratic Formula.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f165503460f94c2b737/html5/thumbnails/12.jpg)
WHY USE THE QUADRATIC FORMULA?
The quadratic formula allows you to
solve ANY quadratic equation, even
if you cannot factor it.
![Page 13: Warm Up. Solving Quadratic Equations by the Quadratic Formula.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f165503460f94c2b737/html5/thumbnails/13.jpg)
Example 2
𝑥2+2𝑥=63Answer:
![Page 14: Warm Up. Solving Quadratic Equations by the Quadratic Formula.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f165503460f94c2b737/html5/thumbnails/14.jpg)
Example 3: You try
𝑥2+8 𝑥−84
• Answer: 6 , -14
![Page 15: Warm Up. Solving Quadratic Equations by the Quadratic Formula.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f165503460f94c2b737/html5/thumbnails/15.jpg)
Example 4: you try again!
• Answer: -3, 8
𝑥2−5 𝑥=24
![Page 16: Warm Up. Solving Quadratic Equations by the Quadratic Formula.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f165503460f94c2b737/html5/thumbnails/16.jpg)
You try! Start with 1 and 4,
then go on to the others.
2
2
2
2
2
1. 2 63 0
2. 8 84 0
3. 5 24 0
4. 7 13 0
5. 3 5 6 0
x x
x x
x x
x x
x x
1. 9,7
2.(6, 14)
3. 3,8
7 34.
2
5 475.
6
i
i
![Page 17: Warm Up. Solving Quadratic Equations by the Quadratic Formula.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f165503460f94c2b737/html5/thumbnails/17.jpg)
Homework:
• 9.7• 1: all• 3: a and b.