Answer:
C.
and ![y=x^2-6x+9](https://tex.z-dn.net/?f=y%3Dx%5E2-6x%2B9)
Step-by-step explanation:
before answering the problem let us remind the formula for square of sum and differences
![(a+b)^2=a^2+2 \times a \times b + b^2](https://tex.z-dn.net/?f=%28a%2Bb%29%5E2%3Da%5E2%2B2%20%5Ctimes%20a%20%5Ctimes%20b%20%2B%20b%5E2)
![(a-b)^2=a^2-2 \times a \times b + b^2](https://tex.z-dn.net/?f=%28a-b%29%5E2%3Da%5E2-2%20%5Ctimes%20a%20%5Ctimes%20b%20%2B%20b%5E2)
We are going to use the above two formulas to solve each part and come to an answer
A. ![y = (x + 3)^2](https://tex.z-dn.net/?f=y%20%3D%20%28x%20%2B%203%29%5E2)
![(x + 3)^2=x^2+2 \times x \times 3 + 3^2](https://tex.z-dn.net/?f=%28x%20%2B%203%29%5E2%3Dx%5E2%2B2%20%5Ctimes%20x%20%5Ctimes%203%20%2B%203%5E2)
![(x + 3)^2=x^2+6x+9](https://tex.z-dn.net/?f=%28x%20%2B%203%29%5E2%3Dx%5E2%2B6x%2B9)
Hence this option is not correct pair
B. ![y = (x-5)^2](https://tex.z-dn.net/?f=y%20%3D%20%28x-5%29%5E2)
![(x - 5)^2=x^2-2 \times x \times 5 + 5^2](https://tex.z-dn.net/?f=%28x%20-%205%29%5E2%3Dx%5E2-2%20%5Ctimes%20x%20%5Ctimes%205%20%2B%205%5E2)
![(x -5)^2=x^2-10x+25](https://tex.z-dn.net/?f=%28x%20-5%29%5E2%3Dx%5E2-10x%2B25)
Hence this option is also not correct pair
C. ![y = (x -3)^2](https://tex.z-dn.net/?f=y%20%3D%20%28x%20-3%29%5E2)
![(x - 3)^2=x^2-2 \times x \times 3 + 3^2](https://tex.z-dn.net/?f=%28x%20-%203%29%5E2%3Dx%5E2-2%20%5Ctimes%20x%20%5Ctimes%203%20%2B%203%5E2)
![(x -3)^2=x^2-6x+9](https://tex.z-dn.net/?f=%28x%20-3%29%5E2%3Dx%5E2-6x%2B9)
Hence this option is correct as it have equivalent pair
D. ![y = (x + 5)^2](https://tex.z-dn.net/?f=y%20%3D%20%28x%20%2B%205%29%5E2)
![(x + 5)^2=x^2+2 \times x \times 5 + 5^2](https://tex.z-dn.net/?f=%28x%20%2B%205%29%5E2%3Dx%5E2%2B2%20%5Ctimes%20x%20%5Ctimes%205%20%2B%205%5E2)
![(x + 5)^2=x^2+10x+25](https://tex.z-dn.net/?f=%28x%20%2B%205%29%5E2%3Dx%5E2%2B10x%2B25)
Hence this option is also not correct pair
The two numbers that add up to get -1 and multiply to get -20 are -5 and 4
-5*4=-20
-5+4=-1
I hope this helps
A) The Y-intercept of this equation is 3
B) The slope of this equation is 2
C) This equation has a positive slope
D) Starting from the Y-intercept, I simply went over to the right 1 box, and up 2 boxes
I hope this helps!
If u tell me the solution's like are u evaluating or what, which method is it i can tell u the answer <span />
Answer:
![\fbox{\begin{minipage}{9em}x = -2 and x = -6\end{minipage}}](https://tex.z-dn.net/?f=%5Cfbox%7B%5Cbegin%7Bminipage%7D%7B9em%7Dx%20%3D%20-2%20and%20x%20%3D%20-6%5Cend%7Bminipage%7D%7D)
Step-by-step explanation:
Given:
![x^{2} + 8x + 12 = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%208x%20%2B%2012%20%3D%200)
Solve for:
![x](https://tex.z-dn.net/?f=x)
Solution:
Step 1: Select the formula to solve for ![x](https://tex.z-dn.net/?f=x)
There are some ways to solve quadratic equations.
One of the simple way (if possible) is performing the factorization.
Another way is using the quadratic formula.
Here, we are going to use factorization.
Step 2: Perform factorization
![x^{2} + 8x + 12 = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%208x%20%2B%2012%20%3D%200)
<=>![x^{2} + 2x + 6x + 12 = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%20%2B%20%202x%20%2B%206x%20%20%2B%2012%20%3D%200)
<=>![(x^{2} + 2x) + (6x + 12) = 0](https://tex.z-dn.net/?f=%28x%5E%7B2%7D%20%2B%202x%29%20%2B%20%286x%20%2B%2012%29%20%3D%200)
<=>![x(x + 2) + 6(x + 2) = 0](https://tex.z-dn.net/?f=x%28x%20%2B%202%29%20%2B%206%28x%20%2B%202%29%20%3D%200)
<=>![(x + 2)(x + 6) = 0](https://tex.z-dn.net/?f=%28x%20%2B%202%29%28x%20%2B%206%29%20%3D%200)
<=>
or ![x = -6](https://tex.z-dn.net/?f=x%20%3D%20-6)
Hope this helps!
:)