Sketch the graph of y=-(x-1)^2 - 2 and it's parent function on the same coordinate grid.

Question

b) Complete the following for the parabola in part a) (the transformed one)

Vertex=

Equation of Axis of symmetry=

Values y may take i.e. Range

Answer 1

The parent function is y = x², which is a parabola with the vertex at the origin (0,0). The axis of symmetry is the vertical line x = 0.

The transformed function is y = -(x-1)² - 2. It has three transformations:

1. the minus sign in front of the (x-1)² flips the parabola upside down, so the vertex is now at the top.
2. The -1 in (x-1)² pushes the parabola 1 unit to the right.
3. The -2 at the end pushes the parabola down 2 units.

The axis of symmetry is unaffected by first and third transformations. The second transformation, however, pushes it to the right 1 unit from x = 0 to x = 1.

The vertex, which was at (0,0) moves right 1 unit and down 2 units to (1, -2).

Since the parabola is now inverted, the largest y value is at the vertex, y = -2. The range is [-2, -∞).