The parabola will show the vertex in the format: y-k = (x-h)^2, where the vertex point
lies at (h, k).
![so \: for \: {x}^{2} + 2x - y + 3 = 0](https://tex.z-dn.net/?f=so%20%5C%3A%20for%20%5C%3A%20%20%7Bx%7D%5E%7B2%7D%20%20%2B%202x%20-%20y%20%2B%203%20%3D%200)
let's first put it in "y =" standard format:
![y = {x}^{2} + 2x + 3](https://tex.z-dn.net/?f=y%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20%2B%202x%20%2B%203)
Since we cannot get a perfect square out of this, we complete the square: a=1, b=2, c=3
(b/2)^2 = (2/2)^2 = 1, so
![y = {(x +1)}^{2} ...\: is \: y = {x}^{2} + 2x + 1](https://tex.z-dn.net/?f=y%20%3D%20%20%7B%28x%20%2B1%29%7D%5E%7B2%7D%20...%5C%3A%20is%20%5C%3A%20y%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20%2B%202x%20%2B%201)
So there's +2 leftover, since 3-1=2; so:
![y = {(x + 1)}^{2} + 2](https://tex.z-dn.net/?f=y%20%3D%20%20%7B%28x%20%2B%201%29%7D%5E%7B2%7D%20%20%2B%202)
Now we'll subtract the 2 from both sides to show our vertex:
![y - 2 = {(x + 1)}^{2}](https://tex.z-dn.net/?f=y%20-%202%20%3D%20%20%7B%28x%20%2B%201%29%7D%5E%7B2%7D%20)
where our vertex (h, k) is at (-1, 2)
D is most likely the answer.
Hope this Helped!
;D
Brainliest??
The answer would be 19
Range is basically just taking the highest and lowest number which in this case is 61 and 42 and then subtracting which gives you 19. Hope this helps!
I'm sorry i don't know what the question is asking for but this is what i get:
for the food to be within the budget:
6x + 4y<span> ≤ 100
6(12) + 4( 5.5) </span><span> ≤ 100
72 + 22 </span><span> ≤ 100
94 </span><span> ≤ 100
with this, they could buy 6 pizzas and 4 sodas, as well as an extra soda
so that's 6 pizzas and 5 sodas to stay under budget.
sorry if i'm wrong</span>
E equals five because seven times five equals 35, minus four equals 31