Question

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

Answer 1

We know that 
the equation of a parabola is of the form
y=a*(x-h)²+k--------> is a vertical parabola
(h,k) is the vertex
y=−14x²+4x−19
Factor the leading coefficient 
y=-14*(x²-4/14x)-19
y=-14*(x²-2/7x)-19
Complete the square  Remember to balance the equation 
y=-14*(x²-2/7x+(1/49)-(1/49))-19
y=-14*(x²-2/7x+(1/49))-19+14/49

Rewrite as perfect squares

y=-14*(x-1/7)²-917/49

the vertex of the parabola is
h=(1/7)-----> 0.1429
k=(-917/49)----> -18.7143

the vertex of the parabola is
(0.1429, -18.7143)

see the attached figure