The equation of a parabola is given. y=−14x2+4x−19 what are the coordinates of the vertex of the parabola?

We know that the equation of a parabola is as:

................(Equation 1)

Where h and k are the coordinates of the vertex of the parabola which is at .

Now, The equation of the parabola given to us is:

..........(Equation 2)

Thus to find the vertex of this parabola, we will have to first convert (Equation 2) to (Equation 1) and find the corresponding value of h and k. For this we will have to complete the square and balance the equation. Let us begin:

..........(Equation 2)

Thus, and

Therefore, the coordinates of the vertex of the parabola are: