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)
Answer:
X = -8
Step-by-step explanation:
Answer:
![x=-4](https://tex.z-dn.net/?f=x%3D-4)
Step-by-step explanation:
we are given equation as
![2x^2+8x=x^2-16](https://tex.z-dn.net/?f=2x%5E2%2B8x%3Dx%5E2-16)
Since, we have to solve for x
so, we will make all terms on left side
add both sides 16
![2x^2+8x+16=x^2-16+16](https://tex.z-dn.net/?f=2x%5E2%2B8x%2B16%3Dx%5E2-16%2B16)
![2x^2+8x+16=x^2](https://tex.z-dn.net/?f=2x%5E2%2B8x%2B16%3Dx%5E2)
Subtract both sides by x^2
![2x^2+8x+16-x^2=x^2-x^2](https://tex.z-dn.net/?f=2x%5E2%2B8x%2B16-x%5E2%3Dx%5E2-x%5E2)
![x^2+8x+16=0](https://tex.z-dn.net/?f=x%5E2%2B8x%2B16%3D0)
now, we can factor it
![(x+4)^2=0](https://tex.z-dn.net/?f=%28x%2B4%29%5E2%3D0)
now, we can solve for x
and we get
![x=-4](https://tex.z-dn.net/?f=x%3D-4)
Answer:
Step-by-step explanation:
x=7 would be horizontal and would be 7 units to the right of the origin, y= -2 would be vertical and 2 units down from the origin