The equation in the vertex form is expressed as
y = - 2(x - 4)^2 + 2
The equation of a parabola in the vertex form is expressed as
y = a(x - h)^2 + k
where
h and k are the vertices of the parabola. By comparing both equations,
a = - 2
h = 4, k = 2
Thus, vertex = (4, 2)
The next step is to find the y intercept. The value of y when x = 0. Thus,
y = - 2(0 - 4)^2 + 2
y = - 2(- 4)^2 + 2 = - 32 + 2
y intercept = - 30
The next step is to find the x intercept. The value of x when y = 0. Thus,
0 = - 2(x - 4)^2 + 2
0 = - 2(x^2 - 8x + 16) + 2
0 = - 2x^2 + 16x - 32 + 2
0 = - 2x^2 + 16x - 30
0 = - 2x^2 + 10x + 6x - 30
0 = - 2x(x - 5) + 6(x - 5)
(x - 5)(- 2x + 6) = 0
x - 5 = 0 or - 2x + 6 = 0
x = 5 or 2x = 6
x = 5 or x = 6/2 = 3
Thus, we would graph the parabola using the above points. the graph is shown below