The given graphs show functions which have been transformed from the quadratic parent, f(x) = x2. determine which transformations were applied to the quadratic parent function to result in each graph.

Answers:

           g(x)                                    h(x)                                     d(x)
vertical shift down 3     reflection across the x-axis     vertical shift down 3
horizontal shift left 3     vertical strecht of 3                 horizontal shift right 3

Quadratic parent: f(x)=x^2
The graph is a parabola with vertex V=(0,0) at the origin and opens up.
When x=1→f(1)=1^2→f(1)=1

1) g(x)
The graph opens up, then there is not a reflection across the x-axis.
The vertex is at the point (-3,-3): 3 units to the left and 3 units down of the vertex of the parent funtion.
When x is 1 unit to the right from the vertex g(x)=1
Then the transformations were applied to the cuadratic parent function are:
1.1) vertical shift down 3.
1.2) horizontal shift left 3.

2) h(x)
The graph opens down, then there is a reflection across the x-axis.
The vertex is at the origin (0,0).
When x is 1 unit to the right from the vertex h(x)=-3
Then the transformations were applied to the cuadratic parent function are:
2.1) reflection across the x-axis.
2.2) vertical strecht of 3.

3) d(x)
The graph opens up, then there is not a reflection across the x-axis.
The vertex is at the point (3,-3): 3 units to the right and 3 units down of the vertex of the parent funtion.
When x is 1 unit to the right from the vertex d(x)=1
Then the transformations were applied to the cuadratic parent function are:
3.1) vertical shift down 3.
3.2) horizontal shift right 3.

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