Question

A parabola opening up or down has vertex (0,0) and passes through (4,2). Write it’s equation in vertex form

Answer 1

Equation in vertex form, y= (-1/4) x² + 4

Step-by-step explanation:

 we have the equation,

y = ax² + 4     ( we need to find "a")

Now we have,

   2 = a(4)2 + 4

   2 = a (8)+ 4

   2-4 = 8a

   -2= 8a

   a= -1/4

Substituting the value of "a" in the equation,  we have

           y = (-1/4)(x- 0)² + 4  (or) y= (-1/4) x² + 4

 The parabola is opens downward. Therefore the vertex is above the x-axis and then the parabola passes through a point below the x-axis.

       Equation in vertex form= y= (-1/4) x² + 4