Check the picture below. So the parabola looks more or less like so.
let's recall that the vertex is half-way between the focus point and the directrix, at "p" units away from both.
Let's notice that the focus point is below the directrix, that means the parabola is vertical, namely the squared variable is the "x", and it also means that it's opening downwards as you see in the picture, namely that "p" is negative, in this case "p" is 1 unit, and thus is -1.
![\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ \stackrel{\textit{we'll use this one}}{4p(y- k)=(x- h)^2} \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-2\\ k=5\\ p=-1 \end{cases}\implies 4(-1)(y-5)=[x-(-2)]^2\implies -4(y-5)=(x+2)^2 \\\\\\ y-5=-\cfrac{1}{4}(x+2)^2\implies y=-\cfrac{1}{4}(x+2)^2+5](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bparabola%20vertex%20form%20with%20focus%20point%20distance%7D%20%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bllll%7D%204p%28x-%20h%29%3D%28y-%20k%29%5E2%20%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bwe%27ll%20use%20this%20one%7D%7D%7B4p%28y-%20k%29%3D%28x-%20h%29%5E2%7D%20%5Cend%7Barray%7D%20%5Cqquad%20%5Cbegin%7Barray%7D%7Bllll%7D%20vertex%5C%20%28%20h%2C%20k%29%5C%5C%5C%5C%20p%3D%5Ctextit%7Bdistance%20from%20vertex%20to%20%7D%5C%5C%20%5Cqquad%20%5Ctextit%7B%20focus%20or%20directrix%7D%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cbegin%7Bcases%7D%20h%3D-2%5C%5C%20k%3D5%5C%5C%20p%3D-1%20%5Cend%7Bcases%7D%5Cimplies%204%28-1%29%28y-5%29%3D%5Bx-%28-2%29%5D%5E2%5Cimplies%20-4%28y-5%29%3D%28x%2B2%29%5E2%20%5C%5C%5C%5C%5C%5C%20y-5%3D-%5Ccfrac%7B1%7D%7B4%7D%28x%2B2%29%5E2%5Cimplies%20y%3D-%5Ccfrac%7B1%7D%7B4%7D%28x%2B2%29%5E2%2B5)
Answer:
Isosoles <em>triangleddndnndnendndne</em>
Blank 1: If y is -5 when x is 2, that means the equation here is y = -2.5x. So, if x is 8, that makes the equation y = -2.5(8), which gives you -20.
Blank 2: If y is 3 when x is 1, the equation will be y = 3x. If x is 2, that will give you y = 3(2), which is 6.
Blank 3: If y is -7 when x is -21, the equation will be x = 3y. If y is 9, that will give you x = 3(9), which is 27.
Blank 4: If y is 5 when x is 4, the equation will be y = 1.25x. If y is 18, that makes the equation 18 = 1.25x, which is 14.4.
I hope this all helped!
In order to solve this exercise you need to remember the following symbols in Inequalities:
1. The meaning of this symbol is "Greater than":
2. The meaning of this one is "Less than":
3. The following symbol means "Less than or equal to":
4. And this one means "Greater than or equal to":
Knowing the above, you can determine that the statement "c is less than 6", can be written as the following inequality:
The answer is:
Answer:
949
Step-by-step explanation:
