Question

What's the equation:

Answer 1

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

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

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

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• 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:

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

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

Thus:

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

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

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

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

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• 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