Check the picture below, so the parabola looks more or less like so, hmmm with a vertex at (-1 , -4), so, using those values from the table
![~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=~~~~~~%5Ctextit%7Bvertical%20parabola%20vertex%20form%7D%20%5C%5C%5C%5C%20y%3Da%28x-%20h%29%5E2%2B%20k%5Cqquad%20%5Cbegin%7Bcases%7D%20%5Cstackrel%7Bvertex%7D%7B%28h%2Ck%29%7D%5C%5C%5C%5C%20%5Cstackrel%7B%22a%22~is~negative%7D%7Bop%20ens~%5Ccap%7D%5Cqquad%20%5Cstackrel%7B%22a%22~is~positive%7D%7Bop%20ens~%5Ccup%7D%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
![\stackrel{vertex}{\stackrel{h}{-1}~~,~~\stackrel{k}{-4}}\qquad \implies y=a[x-(-1)]^2-4\implies y=a(x+1)^2-4 \\\\\\ \textit{we also know that} \begin{cases} x=2\\ y=14 \end{cases}\implies 14=a(2+1)^2-4\implies 18=9a \\\\\\ \cfrac{18}{9}=a\implies 2=a~\hspace{10em}\boxed{y=2(x+1)^2-4}](https://tex.z-dn.net/?f=%5Cstackrel%7Bvertex%7D%7B%5Cstackrel%7Bh%7D%7B-1%7D~~%2C~~%5Cstackrel%7Bk%7D%7B-4%7D%7D%5Cqquad%20%5Cimplies%20y%3Da%5Bx-%28-1%29%5D%5E2-4%5Cimplies%20y%3Da%28x%2B1%29%5E2-4%20%5C%5C%5C%5C%5C%5C%20%5Ctextit%7Bwe%20also%20know%20that%7D%20%5Cbegin%7Bcases%7D%20x%3D2%5C%5C%20y%3D14%20%5Cend%7Bcases%7D%5Cimplies%2014%3Da%282%2B1%29%5E2-4%5Cimplies%2018%3D9a%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B18%7D%7B9%7D%3Da%5Cimplies%202%3Da~%5Chspace%7B10em%7D%5Cboxed%7By%3D2%28x%2B1%29%5E2-4%7D)
The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate.
You can just summarize this if you want.
Hope this helped!
A bicyclist travels at a constant speed of 12 miles per hour for a total of 45 minutes
Domain x is number of hours
Range y is distance traveled
speed = 12 miles per hour
time = 45 minutes =
= 0.75 hours
We know distance formula
Distance = speed * time
Distance = 12 * 0.75= 9 miles
Number of hours x is 0 to 0.75 hours
So domain is {
}
Distance is 0 to 9 miles
So range is {
}
3x^2 + 2x - 6 if x = -2
=3(-2)^2 + 2(-2) - 6
=12 - 4 - 6
= 2
5x^2 + 6x - 2 if x = -2
=5(-2)^2 + 6(-2) - 2
=20 - 12 - 2
= 6
-2x^3 + 2x^2 if x = 2
= -2(2)^3 + 2(2)^2
= -16 + 8
= -8
Answer:
x = 30
Step-by-step explanation:
Let's set up an equation to represent this problem:
2/5 * x + 15 = 27
subtracting 15 from both sides,
2/5 * x = 12
Multiplying 5/2 to both sides,
5/2 * 2/5 * x = 12 * 5/2
1*x = 30
x = 30