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Describe the Graph: The gray graph is y = x². What are the transformations?

Describe the Graph:
The gray graph is y = x².
What are the transformations?
Vertex shift down 5 units and left 3 units.
The vertex?
Axis of symmetry?
Domain does not change.
Range shift down 5 units.
(-4, -3) and (2, -3) are a pair of symmetric points.
Equation? f(x) = (x - )² +

Answer

Transformations: The graph is shifted down 5 units and left 3 units.

Vertex: The vertex is at (-3, -5).

Axis of Symmetry: The axis of symmetry is x = -3.

Domain: The domain remains all real numbers.

Range: The range is y ≥ -5.

Symmetric Points: (-4, -3) and (2, -3) are symmetric about the axis of symmetry.

Equation: f(x) = (x + 3)² - 5

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