Answer:
![y = 5 ( x - 3 ) ^2 -2](https://tex.z-dn.net/?f=y%20%3D%205%20%28%20x%20-%203%20%29%20%5E2%20-2)
OR
![y+2= 5 ( x - 3 ) ^2](https://tex.z-dn.net/?f=y%2B2%3D%205%20%28%20x%20-%203%20%29%20%5E2)
Step-by-step explanation:
Vertex form of a parabola is given as:
![y = a ( x - h ) ^2 + k](https://tex.z-dn.net/?f=y%20%3D%20a%20%28%20x%20-%20h%20%29%20%5E2%20%2B%20k)
Where (
) is the vertex and
are the points on the parabola.
We are given that, the vertex is (3, -2) and another point on parabola is given as (2, 3).
![h = 3,k = -2](https://tex.z-dn.net/?f=h%20%3D%203%2Ck%20%3D%20-2)
First of all, putting the vertex in the vertex equation as given above:
![y = a ( x - 3 ) ^2 + (-2)](https://tex.z-dn.net/?f=y%20%3D%20a%20%28%20x%20-%203%20%29%20%5E2%20%2B%20%28-2%29)
Now, putting the values of
as 2, 3 and let us find the unknown variable
:
![3 = a ( 2 - 3 ) ^2 + (-2)\\\Rightarrow 3 = a -2\\\Rightarrow a = 5](https://tex.z-dn.net/?f=3%20%3D%20a%20%28%202%20-%203%20%29%20%5E2%20%2B%20%28-2%29%5C%5C%5CRightarrow%203%20%3D%20a%20-2%5C%5C%5CRightarrow%20a%20%3D%205)
Therefore, the equation in vertex form can be written as:
![y = 5 ( x - 3 ) ^2 -2](https://tex.z-dn.net/?f=y%20%3D%205%20%28%20x%20-%203%20%29%20%5E2%20-2)
OR
![y+2= 5 ( x - 3 ) ^2](https://tex.z-dn.net/?f=y%2B2%3D%205%20%28%20x%20-%203%20%29%20%5E2)