Question

The vertex of a parabola is (3,-2) and another point on the parabola is (2,3) find the equation of the parabola in vertex form

Answer 1

Answer:

$y = 5 ( x - 3 ) ^2 -2$

OR

$y+2= 5 ( x - 3 ) ^2$

Step-by-step explanation:

Vertex form of a parabola is given as:

$y = a ( x - h ) ^2 + k$

Where ($h,k$) is the vertex and $(x,y)$ 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).

$h = 3,k = -2$

First of all, putting the vertex in the vertex equation as given above:

$y = a ( x - 3 ) ^2 + (-2)$

Now, putting the values of $x, y$ as 2, 3 and let us find the unknown variable $a$:

$3 = a ( 2 - 3 ) ^2 + (-2)\\\Rightarrow 3 = a -2\\\Rightarrow a = 5$

Therefore, the equation in vertex form can be written as:

$y = 5 ( x - 3 ) ^2 -2$

OR

$y+2= 5 ( x - 3 ) ^2$