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Answer:
- vertical scale ×2; translate (-1, -5); (-1, -5), (0, -3), (-2, -3)
- vertical scale ×1/2; translate (3, 1); (3, 1), (1, 3), (5, 3)
- reflect over x; vertical scale ×2; translate (-3, -4); (-3, -4), (-2, -6), (1, -8)
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.
1.
(c, h, k) = (2, -1, -5)
- vertical scaling by a factor of 2
- translation 1 left and down 5
Points: (-1, -5), (-2, -3), (0, -3)
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2.
(c, h, k) = (1/2, 3, 1)
- vertical scaling by a factor of 1/2
- translation 3 right and 1 up
Points: (3, 1), (1, 3), (5, 3)
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3.
(c, h, k) = (-2, -3, -4)
- reflection over the x-axis
- vertical scaling by a factor of 2
- translation 3 left and 4 down
Points: (-3, -4), (-2, -6), (1, -8)
_____
Additional comment
For finding points on the parabolas, we use our knowledge of squares and roots:
1² = 1, 2² = 4
√1 = 1, √4 = 2
