Check the picture below.
so the focus point is there, and the directrix is above it, meaning is a vertical parabola and is opening downwards, since the parabola opens up towards the focus.
now, the vertex is half-way between those two guys, at a "p" distance from either one, if we move over the y-axis from -5 to +2, we have 7 units, half-way is 3.5 units, and that puts us at -1.5 or -1½, as you see in the picture, so the vertex is then at (-3 , -1½).
so the distance from the vertex to the focus point is then 3½ units, however since the parabola is opening downwards, "p" is negative, thus "p = 3½".
![\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ \stackrel{\textit{using 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}](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%7Busing%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)
![\bf \begin{cases} h=-3\\ k=-\frac{3}{2}\\[0.7em] p=-\frac{7}{2} \end{cases}\implies 4\left( -\cfrac{7}{2} \right)\left[ y-\left(-\cfrac{3}{2} \right) \right]=\left[ x-\left( -3 \right) \right]^2 \\\\\\ -14\left( y+\cfrac{3}{2} \right)=(x+3)^2\implies y+\cfrac{3}{2} =-\cfrac{(x+3)^2}{14} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=-\cfrac{1}{14}(x+3)^2-\cfrac{3}{2}~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%20h%3D-3%5C%5C%20k%3D-%5Cfrac%7B3%7D%7B2%7D%5C%5C%5B0.7em%5D%20p%3D-%5Cfrac%7B7%7D%7B2%7D%20%5Cend%7Bcases%7D%5Cimplies%204%5Cleft%28%20-%5Ccfrac%7B7%7D%7B2%7D%20%5Cright%29%5Cleft%5B%20y-%5Cleft%28-%5Ccfrac%7B3%7D%7B2%7D%20%5Cright%29%20%5Cright%5D%3D%5Cleft%5B%20x-%5Cleft%28%20-3%20%5Cright%29%20%5Cright%5D%5E2%20%5C%5C%5C%5C%5C%5C%20-14%5Cleft%28%20y%2B%5Ccfrac%7B3%7D%7B2%7D%20%5Cright%29%3D%28x%2B3%29%5E2%5Cimplies%20y%2B%5Ccfrac%7B3%7D%7B2%7D%20%3D-%5Ccfrac%7B%28x%2B3%29%5E2%7D%7B14%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20y%3D-%5Ccfrac%7B1%7D%7B14%7D%28x%2B3%29%5E2-%5Ccfrac%7B3%7D%7B2%7D~%5Chfill)
In the load of 3/4 ton of steel rods 1/8 of them are bent
then you divided 1/8 by 3 and get 1/24 because thats only 75% of the ton
so about 4/24 or 1/6 of it is bent
Answer: 4.14 m.
Step-by-step explanation:
<h2>
Hello!</h2>
The answer is:
A) The solution to the inequality is all the values of "x" less than -3.
<h2>Why?</h2>
To solve the problem, we must remember that isolating variables from inequalities and equalities are almost the same, however, we must remember that the solutions to both have completely different meanings.
Inequalities usually are used to express where a determined function exists, and are referred to restrictions or conditions.
So, we are given the following inequality:
Then, solving we have:
Hence, the solution to the inequality are all the values of "x" less than -3.
It can be also written like: (-∞,-3)
So, the correct option is the last graph:
A) The solution to the inequality is all the values of "x" less than -3.
Have a nice day!
Answer:
8 daisies
Step-by-step explanation:
You have to multiply the amount of vases by daisies.
