Answer:![x^2-5x=-12(y+2)](https://tex.z-dn.net/?f=x%5E2-5x%3D-12%28y%2B2%29)
Step-by-step explanation:
Given
Parabola has x-intercept has
and ![(8,0)](https://tex.z-dn.net/?f=%288%2C0%29)
and Y-intercept as ![(0,-2)](https://tex.z-dn.net/?f=%280%2C-2%29)
Now the general equation of parabola is
![y=ax^2+bx+c\quad \ldots(i)](https://tex.z-dn.net/?f=y%3Dax%5E2%2Bbx%2Bc%5Cquad%20%5Cldots%28i%29)
Substitute
in
we get
![-2=c](https://tex.z-dn.net/?f=-2%3Dc)
Now substitute
in equation ![(i)](https://tex.z-dn.net/?f=%28i%29)
![0=a(3)^2+3b-2\quad \ldots(ii)](https://tex.z-dn.net/?f=0%3Da%283%29%5E2%2B3b-2%5Cquad%20%5Cldots%28ii%29)
Now substitute
in equation ![(i)](https://tex.z-dn.net/?f=%28i%29)
![0=a(8)^2+8b-2\quad \ldots(iii)](https://tex.z-dn.net/?f=0%3Da%288%29%5E2%2B8b-2%5Cquad%20%5Cldots%28iii%29)
Solving
and
we get
![a=\frac{-1}{12}\ \text{and}\ b=\frac{5}{12}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B-1%7D%7B12%7D%5C%20%5Ctext%7Band%7D%5C%20b%3D%5Cfrac%7B5%7D%7B12%7D)
therefore
![y=\frac{-x^2}{12}+\frac{5x}{12}-2](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-x%5E2%7D%7B12%7D%2B%5Cfrac%7B5x%7D%7B12%7D-2)
![12y=-x^2+5x-24](https://tex.z-dn.net/?f=12y%3D-x%5E2%2B5x-24)
When we have negative exponents, we can move the term with the exponent to the bottom of the fraction. This is also known as multiplying by the reciprocal (and changing the negative exponent to be positive!).
The reciprocal of z^-3 would be 1 / z^3.
Hope this helps!! :)
Identity Property of Zero!
I hope this helps xD
B.) 8(x+4) is the best choice
Answer:
k=1
Step-by-step explanation:
![3k + 8 = 11\\](https://tex.z-dn.net/?f=3k%20%2B%208%20%3D%2011%5C%5C)
Subtract 8 from both sides
![3k = 3](https://tex.z-dn.net/?f=3k%20%3D%203)
Divide
![\frac{3k}{3} = \frac{3}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3k%7D%7B3%7D%20%3D%20%5Cfrac%7B3%7D%7B3%7D)
Simplify
![k =1](https://tex.z-dn.net/?f=k%20%3D1)