find both coordinates of the vertex of the parabola

Question

g(x) = -2x^2 + 2x - 5.

Answer 1

Given parabola g(x) = -2x^2+2x-5

Compare it standard parabola form y = ax^2+bx+c

a = -2, b = 2, c = -5.

Axis of symmetry x = -b/2a = -2/-4

x = 1/2

To find vertex substitute x value in given equation.

y = -2(1/2)^2+2(1/2)-5

y = -2(1/4)+1-5

y = -1/2-4

y = (-1-8)/2

y = -9/2

Vertex of parabola = (1/2,-9/2).