Answer:
[tex]y = 5 ( x - 3 ) ^2 -2[/tex]
OR
[tex]y+2= 5 ( x - 3 ) ^2[/tex]
Step-by-step explanation:
Vertex form of a parabola is given as:
[tex]y = a ( x - h ) ^2 + k[/tex]
Where ([tex]h,k[/tex]) is the vertex and [tex](x,y)[/tex] 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).
[tex]h = 3,k = -2[/tex]
First of all, putting the vertex in the vertex equation as given above:
[tex]y = a ( x - 3 ) ^2 + (-2)[/tex]
Now, putting the values of [tex]x, y[/tex] as 2, 3 and let us find the unknown variable [tex]a[/tex]:
[tex]3 = a ( 2 - 3 ) ^2 + (-2)\\\Rightarrow 3 = a -2\\\Rightarrow a = 5[/tex]
Therefore, the equation in vertex form can be written as:
[tex]y = 5 ( x - 3 ) ^2 -2[/tex]
OR
[tex]y+2= 5 ( x - 3 ) ^2[/tex]
