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9514 1404 393
Answer:
y = 3x^2 +30x +69
Step-by-step explanation:
Transformations work this way:
g(x) = k·f(x) . . . . vertical stretch by a factor of k
g(x) = f(x -h) +k . . . . translation (right, up) by (h, k)
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So, the translation down 2 units will make the function be ...
f(x) = x^2 ⇒ f1(x) = f(x) -2 = x^2 -2
The vertical stretch by a factor of 3 will make the function be ...
f1(x) = x^2 -2 ⇒ 3·f1(x) = f2(x) = 3(x^2 -2)
The horizontal translation left 5 units will make the function be ...
f2(x) = 3(x^2 -2) ⇒ f2(x +5) = f3(x) = 3((x +5)^2 -2)
The transformed function equation can be written ...
y = 3((x +5)^2 -2) = 3(x^2 +10x +25 -2)
y = 3x^2 +30x +69
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The attachment shows the original function and the various transformations. Note that the final function is translated down 6 units from the original. That is because the down translation came <em>before</em> the vertical scaling.
