Consider the function fx 2x2 4x2 A Determine the vertex of t

Consider the function f(x) -2x² +4x-2

A) Determine the vertex of the graph of this function

B) Write the function in the form f(x)= a(x-h)² +k

C) Explain the shifts or reflections of the graph of y=f(x), relative to y=x²

D) Determine the value of x, that results in the maximum value of f(x)

E) What is the maximum value of the function?

F) What are the x intercepts of the graph of the function?

G) For what intervals in the domain of f, is f(x) < 0?

H) For what intervals in the domain of f, is f(x) > 0?

f(x)= -2x^2 +4x-2

a) Vertex: x= -b/2a = -(4/2*(-2)) =1

Plug x= 1 in f(x) = -2 +4 -2 = 0

Vertex = ( 1, 0)

b) f(x) = -2( x^2 -2x+ 1 -1) -2

= -2(x -1)^2+ 2 -2

f(x) = -2(x-1)^2

c) w.r.t to f(x) = x^2

f(x) is horizontally shifted right by 1 unit y = (x -1)^2

f(x) is vertically shifted by 2 units y = 2( x-1)^2

f(x) is reflected along x axis y = -2(x -1)^2

d) The x coordinate gives the maximum vale x= 1

e) Maximum value at x= 1 f(x) =0

f) X intercept: y=0 ; (x-1)^2 =0---> x =1