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My name is Ann [436]
3 years ago
15

What's the equation:

Mathematics
1 answer:
ElenaW [278]3 years ago
8 0

Using shifting concepts, it is found that the function g is:

g(x) = -9x^2 - 198x - 1085

-------------------------

  • The parent function is f(x) = x^2.

-------------------------

  • Horizontally stretching a function by a factor of b is the finding f(\frac{x}{b}).
  • Thus, horizontally stretching by a factor of 1/3, we have:

g(x) = f(\frac{x}{\frac{1}{3}}) = f(3x) = (3x)^2 = 9x^2

-------------------------

  • Reflecting vertically is finding -f(x)
  • Reflecting horizontally is finding f(-x).

Thus:

g(x) = -9(-x)^2 = -9x^2

-------------------------

  • Translating a units to the left is finding f(x + a), thus:
  • Translating 11 units to the left is finding f(x + 11), thus:

g(x) = -9(x + 11)^2 = -9(x^2 + 22x + 121) = -9x^2 - 198x - 1089

-------------------------

  • Shifting a units up is finding f(x) + a, thus:
  • 4 units up is finding f(x) + 4, thus:

g(x) = -9x^2 - 198x - 1089 + 4 = -9x^2 - 198x - 1085

A similar problem is given at brainly.com/question/23325498

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