PLS PLS help!
Type an equation of a parabola that is moved down 2 units, stretched vertically by a factor of 3, and moved left 5 units.

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 before the vertical scaling.

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