Warm Up Identify the Roots and the Zeros of this quadratic.
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Transcript of Warm Up Identify the Roots and the Zeros of this quadratic.
![Page 1: Warm Up Identify the Roots and the Zeros of this quadratic.](https://reader036.fdocuments.us/reader036/viewer/2022082713/5697bfd11a28abf838caae50/html5/thumbnails/1.jpg)
Warm Up4
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Identify the Roots and the Zeros of this quadratic.
![Page 2: Warm Up Identify the Roots and the Zeros of this quadratic.](https://reader036.fdocuments.us/reader036/viewer/2022082713/5697bfd11a28abf838caae50/html5/thumbnails/2.jpg)
Solving Quadratics by Factoring
![Page 3: Warm Up Identify the Roots and the Zeros of this quadratic.](https://reader036.fdocuments.us/reader036/viewer/2022082713/5697bfd11a28abf838caae50/html5/thumbnails/3.jpg)
• To “solve” a quadratic means to find the roots.
• Easy when you have a graph (just look at the points where it crosses the x-axis)
• But we will solve just from the equation
![Page 4: Warm Up Identify the Roots and the Zeros of this quadratic.](https://reader036.fdocuments.us/reader036/viewer/2022082713/5697bfd11a28abf838caae50/html5/thumbnails/4.jpg)
3 Steps to Solve quadratics
1. Set equation equal to zero2. Factor3. Set each factor equal to 0 and solve
![Page 5: Warm Up Identify the Roots and the Zeros of this quadratic.](https://reader036.fdocuments.us/reader036/viewer/2022082713/5697bfd11a28abf838caae50/html5/thumbnails/5.jpg)
Example 1
Step 1: Rearrange the terms to have zero on one side:
2 22 15 2 15 0x x x x
![Page 6: Warm Up Identify the Roots and the Zeros of this quadratic.](https://reader036.fdocuments.us/reader036/viewer/2022082713/5697bfd11a28abf838caae50/html5/thumbnails/6.jpg)
Continued…
Step 2: Factor
(x+5)(x-3)
![Page 7: Warm Up Identify the Roots and the Zeros of this quadratic.](https://reader036.fdocuments.us/reader036/viewer/2022082713/5697bfd11a28abf838caae50/html5/thumbnails/7.jpg)
Continued
So the roots are x = -5 or x = 3
Step 3:Set each factor equal to zero and solve:
( 5) 0 and ( 3) 0
5 3
x x
x x
![Page 8: Warm Up Identify the Roots and the Zeros of this quadratic.](https://reader036.fdocuments.us/reader036/viewer/2022082713/5697bfd11a28abf838caae50/html5/thumbnails/8.jpg)
Factors, Roots, Zeros
y x2 2x 15For our Polynomial Function:
The Factors are: (x + 5) & (x - 3)
The Roots/Solutions are: x = -5 and 3
The Zeros are at: (-5, 0) and (3, 0)
![Page 9: Warm Up Identify the Roots and the Zeros of this quadratic.](https://reader036.fdocuments.us/reader036/viewer/2022082713/5697bfd11a28abf838caae50/html5/thumbnails/9.jpg)
• What do you notice about the relationship between factors and solutions?
• All you have to do is switch the sign!
• If the factor is (x+1) then the solution is -1.Easy!
![Page 10: Warm Up Identify the Roots and the Zeros of this quadratic.](https://reader036.fdocuments.us/reader036/viewer/2022082713/5697bfd11a28abf838caae50/html5/thumbnails/10.jpg)
Example 2
𝑎2− 2𝑎=−1
• Factors are (x+2)(x-1)
• Solutions/roots are -2 and 1
• Zeros are (-2,0) and (1,0)
![Page 11: Warm Up Identify the Roots and the Zeros of this quadratic.](https://reader036.fdocuments.us/reader036/viewer/2022082713/5697bfd11a28abf838caae50/html5/thumbnails/11.jpg)
You try!
Solutions are -5 and -3
![Page 12: Warm Up Identify the Roots and the Zeros of this quadratic.](https://reader036.fdocuments.us/reader036/viewer/2022082713/5697bfd11a28abf838caae50/html5/thumbnails/12.jpg)
Homework