Question

a parabola opens upward. the parabola goes through the point (3, -1), and the vertex is at (2, -2). what are the values of h and v?

Answer 1

I'm not sure what the v is supposed to stand for but better vertex form of a parabola is y=a(x-h)^2+k

Your vertex is represented by (h,k) so your value for h would be 2.

Answer 2

Answer with explanation:

The Information about the given Parabola:

→Opens Upward

→Passes through the point (3,-1).

→Vertex is at (2,-2).

Equation of Parabola , having vertex at , (2,-2) and opening Upwards is given by:

 $\Rightarrow (x-2)^2=4 a(y+2)$

The Parabola passes through the point (3,-1).

      $\Rightarrow (3-2)^2=4 a(-1+2)\\\\\Rightarrow 1=4 a\\\\\Rightarrow a=\frac{1}{4}$

So,Required Equation of Parabola will be

    $\Rightarrow (x-2)^2=4 \times \frac{1}{4}(y+2)\\\\\Rightarrow (x-2)^2=y+2$

Center of the Parabola called focus will be

     $\Rightarrow h=2\\\\k=-2 + \frac{1}{4}\\\\k=\frac{-7}{4}\\\\\text{Center} =(h,k)\\\\=(2,\frac{-7}{4})$