Answer:
2![\sqrt{13}](https://tex.z-dn.net/?f=%5Csqrt%7B13%7D)
Step-by-step explanation:
Using the distance formula,
![\sqrt{( x_{2}-x_{1} )^2+(y_{2} -y_{1})^2 }](https://tex.z-dn.net/?f=%5Csqrt%7B%28%20x_%7B2%7D-x_%7B1%7D%20%29%5E2%2B%28y_%7B2%7D%20-y_%7B1%7D%29%5E2%20%7D)
We just need to plug in the numbers.
So ![\sqrt{(-1-5)^2+(-2-2)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-1-5%29%5E2%2B%28-2-2%29%5E2%7D)
Then we simplify it to
![\sqrt{(-6)^2+(-4)^2} , to \sqrt{36+16}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-6%29%5E2%2B%28-4%29%5E2%7D%20%2C%20to%20%5Csqrt%7B36%2B16%7D)
Finally, we get
, which is
when simplified.
B. (4, 4) is a solution to the equation.
State the vertex and axis of symmetry of the graph of y=ax^2+c
General form of quadratic equation is ![y=ax^2 + bx +c](https://tex.z-dn.net/?f=y%3Dax%5E2%20%2B%20bx%20%2Bc)
There is no bx in our given equation, so we put 0x
Given equation can be written as ![y=ax^2 + 0x +c](https://tex.z-dn.net/?f=y%3Dax%5E2%20%2B%200x%20%2Bc)
a=a , b=0
Now we use formula to find vertex
![x=\frac{-b}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%7D%7B2a%7D)
![x=\frac{-0}{2a}=0](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-0%7D%7B2a%7D%3D0)
Now we plug in 0 for 'a' and find out y
![y=a(0)^2 + 0x +c= c](https://tex.z-dn.net/?f=y%3Da%280%29%5E2%20%2B%200x%20%2Bc%3D%20c)
So our vertex is (0,c)
The axis of symmetry at x coordinate of vertex
So x=0 is our axis of symmetry
The perimeter will change by the same factor Answer