Find the x-intercepts and the y-intercept of the parabola

Question

Solve the below:

Q: Below concerns the parabola which is the graph of the function

f(x) =((x-2)²/4)-1

a) Explain how the graph of the parabola can be obtained from the graph of y =x² by using appropriate translation and scalings.

b) Using your answer to part (a), or otherwise, write down the coordinates of the vertex of the parabola.

c) Find the x-intercepts and the y-intercept of the parabola.

d) Sketch the parabola, giving the coordinates of the vertex and of the points at which the graph crosses the axes.

e) Write down the equation of the axis of symmetry of the parabola.

f) What is the image set of the function f?