Answer:
![y = {x}^{2} - 2](https://tex.z-dn.net/?f=y%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20-%202)
Or if you want with the value of h too.
![y = {(x - 0)}^{2} - 2](https://tex.z-dn.net/?f=y%20%3D%20%20%7B%28x%20-%200%29%7D%5E%7B2%7D%20%20-%202)
Step-by-step explanation:
![y = a {(x - h)}^{2} + k](https://tex.z-dn.net/?f=y%20%3D%20a%20%7B%28x%20-%20h%29%7D%5E%7B2%7D%20%20%2B%20k)
Find the value of h and k by using the formula.
![h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a}](https://tex.z-dn.net/?f=h%20%3D%20%20-%20%20%5Cfrac%7Bb%7D%7B2a%7D%20%20%5C%5C%20k%20%3D%20%20%5Cfrac%7B4ac%20-%20%20%7Bb%7D%5E%7B2%7D%20%7D%7B4a%7D%20)
From y = x²-2
![a = 1 \\ b = 0 \\ c = - 2](https://tex.z-dn.net/?f=a%20%3D%201%20%5C%5C%20b%20%3D%200%20%5C%5C%20c%20%3D%20%20-%202)
Substitute these values in the formula.
![h = - \frac{0}{2(1)} \\ h = 0](https://tex.z-dn.net/?f=h%20%3D%20%20-%20%20%5Cfrac%7B0%7D%7B2%281%29%7D%20%20%5C%5C%20h%20%3D%200)
Therefore, h = 0.
![k = \frac{4(1)( - 2) - {0}^{2} }{4(1)} \\ k = \frac{ - 8}{4} \\ k = - 2](https://tex.z-dn.net/?f=k%20%3D%20%20%5Cfrac%7B4%281%29%28%20-%202%29%20-%20%20%7B0%7D%5E%7B2%7D%20%7D%7B4%281%29%7D%20%20%5C%5C%20k%20%3D%20%20%5Cfrac%7B%20-%208%7D%7B4%7D%20%20%5C%5C%20k%20%3D%20%20-%202)
Therefore, k = - 2.
From the vertex form, the vertex is at (h, k) = (0,-2). Substitute h = 0, a = 1 and k = -2 in the equation.
![y = a {(x - h)}^{2} + k \\ y = 1 {(x - 0)}^{2} - 2 \\ y = {(x)}^{2} - 2 \\ y = {x}^{2} - 2](https://tex.z-dn.net/?f=y%20%3D%20a%20%7B%28x%20-%20h%29%7D%5E%7B2%7D%20%20%2B%20k%20%5C%5C%20y%20%3D%201%20%7B%28x%20-%200%29%7D%5E%7B2%7D%20%20-%202%20%5C%5C%20y%20%3D%20%20%7B%28x%29%7D%5E%7B2%7D%20%20-%202%20%5C%5C%20y%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20-%202)
These type of equation where b = 0 can also be both standard and vertex form.
Answer:
linear
Step-by-step explanation:
y - x = 2x - ![\frac{2y}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2y%7D%7B3%7D)
= 3x
y = 9x/5
The quadrilateral is a square
<h3>What are quadrilaterals?</h3>
Quadrilaterals are polygons, that have four sides and four corners
The coordinates are given as:
- A = (3, 5)
- B = (5, 2)
- C = (8, 4)
- D = (6, 7)
Start by calculating the adjacent side lengths using:
![d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2%20-%20y_1%29%5E2%7D)
So, we have:
![AB = \sqrt{(3- 5)^2 + (5- 2)^2}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%283-%205%29%5E2%20%2B%20%285-%202%29%5E2%7D)
![AB = \sqrt{13}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B13%7D)
![BC = \sqrt{(8- 5)^2 + (4- 2)^2}](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B%288-%205%29%5E2%20%2B%20%284-%202%29%5E2%7D)
![BC = \sqrt{13}](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B13%7D)
The side lengths are equal.
Hence, the quadrilateral is a square
Read more about quadrilaterals at:
brainly.com/question/5715879
186.99999992 and that is the correct anwser i think