Help on graph of f?

Question

f(x)-1/3(x-2)^2-3

a) Explain how the parabola that is the graph of f obtained from graph of y=x^2 using appropriate translations and scaling

b) Using (a) what are the coords of the vertex

c) find the x-intercepts and y-intercept

d) What is the image set of f (interval notation)

Thanks for any help

Answer 1

replacing x by x-2 shifts the vertex 2 units to the right.
Adding -3 shifts the vertex downward 3 units
Multiplying by -1 reflects the parabola across the x-axis.
Dividing by 3 stretches the parabola horizontally.

vertex = (2,-3)

No x - intercepts. y-intercept is - 4 1/3

y =< 3

Answer 2

Ms X , watch your typing, as you have no function description. Was it to f(x) = 1/3 or f(x) = -1/3.If it is the first then you need to modify "ironduke's" answer.