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How are the graphs of f(x) = -x^2 and g(x) = -(x + 2)^2 - 4 related?

1) How are the graphs of f(x) = -x^2 and g(x) = -(x + 2)^2 - 4 related?
Describe the transformation of the parent function f(x) = -x^2
2) g(x) = -(x + 5)^2 + 2
3) f(x) = (x - 2)^2 - 7
4) The graph of the function f(x) = x^2 is translated 3 units up and 1 unit left. What is the resulting function?
Describe the function transformation of the parent function f(x) = x^2. Then graph the transformed function.
5) f(x) = (x - 1)^2 + 3
6) y = (x + 1)^2 - 3

Answer

  1. The graph of g(x) = -(x + 2)^2 - 4 is a horizontal translation 2 units to the left and a vertical translation 4 units down of the graph of f(x) = -x^2.

  2. The function g(x) = -(x + 5)^2 + 2 is a horizontal translation 5 units to the left and a vertical translation 2 units up of the parent function f(x) = -x^2.

  3. The function f(x) = (x - 2)^2 - 7 is a horizontal translation 2 units to the right and a vertical translation 7 units down of the parent function f(x) = x^2.

  4. The resulting function after translating f(x) = x^2, 3 units up and 1 unit left is f(x) = (x + 1)^2 + 3.

  5. The function f(x) = (x - 1)^2 + 3 is a horizontal translation 1 unit to the right and a vertical translation 3 units up of the parent function f(x) = x^2.

  6. The function y = (x + 1)^2 - 3 is a horizontal translation 1 unit to the left and a vertical translation 3 units down of the parent function f(x) = x^2.

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