What is the vertex of #y= -2(x - 4)^2 - 5x+3 #?
The vertex is
One of the forms of the equation of a parabola is
Factor out 2 being the coefficient of
Complete the square: Divide by 2 the coefficient of x and then square the result. The resulting value becomes the constant of the perfect square trinomial.
We need to add 121/16 to form a perfect square trinomial. We have to deduct it as well though, to preserve the equality. The equation now becomes
Isolate the terms which form the perfect square trinomial
Hence, the vertex is