equation of parabola if axis Y=0; passes through (3,2)&(2,-3)

Question

equation of parabola if axis Y=0; passes through (3,2)&(2,-3)

Answer 1

Since the axis of the parabola is horizontal. an equation of the parabola is (y-k)² = 4p(x-h), where (h,k) is the vertex.  

 

The vertex lies on the axis of the parabola, so k must be 0.  

 

So, we have y² = 4p(x-h)

 

Since (3,2) is on the graph, 4 = 4p(3-h)

Since (2,-3) is on the graph, 9 = 4p(2-h)

 

So, 4/(3-h) = 9/(2-h)

 

     8-4h = 27-9h

 

        5h = 19

 

         h = 19/5    So, y² = 4p(x - 19/5)

 

        Since (3,2) is on the graph, 4 = 4p(3 - 19/5)

 

                                               4 = 4p(-4/5)    

 

        Therefore, 4p = (-5/4)(4) = -5

 

        Equation:  y² = -5(x - 19/5)   (or y² = 19 - 5x)