Answered

What is the equation of the translated function, g(x), if
f(x) = x2?

g(x) = (x + 5)2 + 2
g(x) = (x + 2)2 + 5
g(x) = (x – 2)2 + 5
g(x) = (x – 5)2 + 2
On a coordinate plane, two parabolas open up. The solid-line parabola, labeled f of x, goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). The dashed-line parabola, labeled g of x, goes through (3, 6), has a vertex at (5, 2), and goes through (7, 6).



Answer :

sqdancefan

Answer:

  (d)  g(x) = (x – 5)² + 2

Step-by-step explanation:

You want the equation of the parabola f(x) = x² after its vertex has been translated to (5, 2).

Translation

Translation of function f(x) by (h, k) makes the function be ...

  g(x) = f(x -h) +k

When the vertex of f(x) = x² has been translated by (5, 2), it becomes ...

  g(x) = f(x -5) +2

  g(x) = (x -5)² +2 . . . . . matches choice D

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Additional comment

Translation by (h, k) moves the graph h units to the right and k units up. We only need to know how one point is translated in order to know what the translated function is. It is convenient to use the vertex as that reference point.

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