NO LINKS Draw sketches (including several accurate point coordinates) for the following functions. Name all of the transformations.

1. y = 2(x + 1)^2 - 5

2. y = 1/2(x - 3)^2 + 1

3.

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Step-by-step explanation:

Transformation of parent function f(x) into g(x) = c·f(x-h)+k is a vertical scaling by a factor of c, and translation by (h, k) units to the right and up. If c is negative, then a reflection over the x-axis is also part of the transformation. Once you identify the parent function (here: x² or √x), it is a relatively simple matter to read the values of c, h, k from the equation and list the transformations those values represent.

For most functions, points differing from the vertex by 1 or 2 units are usually easily found. Of course, the vertex is one of the points on the function.

  (c, h, k) = (2, -1, -5)

Points: (-1, -5), (-2, -3), (0, -3)

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  (c, h, k) = (1/2, 3, 1)

Points: (3, 1), (1, 3), (5, 3)

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  (c, h, k) = (-2, -3, -4)

Points: (-3, -4), (-2, -6), (1, -8)

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Additional comment

For finding points on the parabolas, we use our knowledge of squares and roots:

  1² = 1, 2² = 4

  √1 = 1, √4 = 2

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step-by-step explanation: