What is the vertex form of this parabola?

Question

Vertex (-1,10) Focus (-1, 41/4)

Answer 1

The vertex (-1, 10) and focus (-1, 41/4)

Since the x coordinate of the vertex and focus are the same,

So this is vertical parabola where x  part is squred.

If a parabola has a vertical axis, the standard form of the equation of the parabola is this:

(x - h )² = 4p(y - k ) , where p ≠ 0 .

The vertex of this parabola is at (h, k ) .

The focus is at (h, k + p ) . The directrix is the line y = k - p .

The axis is the line x = h . If p > 0 , the parabola opens upward, and if p < 0 , the parabola opens downward.

(h, k + p ) = (-1, 41/4)

k + p = 41/4 ---> (1)

(h , k ) = (-1, 10)

k  = 10 ---> (2)

From equation (2) substitute the k  value in equation (1).

10 + p  = 41/4 

p  = (41/4) - 10

p  = (41 - 40)/4

p  = 1/4

p  is posiitive then parabola that opens upward.

The parabola equation is  (x - h )² = 4p (y - k )

Substitute the values (h, k ) = (-1, 10) and 4p = 1 in above equation.

The parabola equation is (x + 1)²= (y - 10).