Answer:
![y = (x - 3)^2 - 12](https://tex.z-dn.net/?f=y%20%3D%20%28x%20-%203%29%5E2%20-%2012)
![(3,-12)](https://tex.z-dn.net/?f=%283%2C-12%29)
Step-by-step explanation:
Given
![y = x^2 - 6x - 3](https://tex.z-dn.net/?f=y%20%3D%20x%5E2%20-%206x%20-%203)
Solving (a): In vertex form
The vertex form of an equation is:
![y = a(x - h)^2 + k](https://tex.z-dn.net/?f=y%20%3D%20a%28x%20-%20h%29%5E2%20%2B%20k)
To do this, we make use of completing the square method.
We have:
![y = x^2 - 6x - 3](https://tex.z-dn.net/?f=y%20%3D%20x%5E2%20-%206x%20-%203)
------------------------------------------------------------------
Take the coefficient of x (i.e. -6)
Divide by 2; -6/2 = -3
Square it: (-3)^2 = 9
Add and subtract the result to the equation
------------------------------------------------------------------
![y = x^2 - 6x - 3](https://tex.z-dn.net/?f=y%20%3D%20x%5E2%20-%206x%20-%203)
![y = x^2 - 6x + 9 - 9 - 3](https://tex.z-dn.net/?f=y%20%3D%20x%5E2%20-%206x%20%2B%209%20-%209%20-%203)
![y = x^2 - 6x + 9 - 12](https://tex.z-dn.net/?f=y%20%3D%20x%5E2%20-%206x%20%2B%209%20-%2012)
Factorize ![x^2 - 6x + 9](https://tex.z-dn.net/?f=x%5E2%20-%206x%20%2B%209)
![y = x^2 - 3x-3x + 9 - 12](https://tex.z-dn.net/?f=y%20%3D%20x%5E2%20-%203x-3x%20%2B%209%20-%2012)
![y = x(x - 3)-3(x - 3) - 12](https://tex.z-dn.net/?f=y%20%3D%20x%28x%20-%203%29-3%28x%20-%203%29%20-%2012)
Factor out x - 3
![y = (x - 3)(x - 3) - 12](https://tex.z-dn.net/?f=y%20%3D%20%28x%20-%203%29%28x%20-%203%29%20-%2012)
Express as squares
![y = (x - 3)^2 - 12](https://tex.z-dn.net/?f=y%20%3D%20%28x%20-%203%29%5E2%20-%2012)
Hence, the vertex form of
is: ![y = (x - 3)^2 - 12](https://tex.z-dn.net/?f=y%20%3D%20%28x%20-%203%29%5E2%20-%2012)
Solving (b): State the coordinates of the vertex.
In
; the vertex is: (h,k)
The vertex of
will be ![(3,-12)](https://tex.z-dn.net/?f=%283%2C-12%29)
<7 = <2 (Alternate exterior angles)
3x + 10 = 70
3x = 60
x = 20
Answer is the 2nd one
20
4.50x + 10
X = the amount of pair of socks you buy
Answer:
28 1/32 ft pieces
Step-by-step explanation:
To solve this problem you need to get both the fractions to have same denominator, to do this we will times 7/8 by 4 to get 28/32. After this we can start comparing them. From the 28/32 we can make 28 pieces because 28*1/32=28/32
Answer:
*44+44468
Step-by-step explanation:
54+85588255)(5(5))55)5)