Question

Find the vertex of f(x)=-2x^2+2x-3
Find the Vertex (h,k)
h= a(x-h)^2+k
and y and x intercepts.

Answer 1

an easier way is o find the line of symmetry x = -b/2a

in your question the line of symmetry is -2/(2 x -2) x = 1/2

then sub into the original equation to find the vertex

y=-2 x(1/2)^2 + 2(1/2) - 3 y = -5/2

so the vertex is (1/2, -5/2)

using in the required form y = -2(x - 1/2)^2 - 5/2

y intercept is when x = 0 so y intercept is y = -3

x intercepts, y = 0

or -2x^2 + 2x -3 = 0

the curve is negative definite so no x intercepts