Question

Describe the translation. y = (x-5)squared +5 - y = (x-))squared +0

Answer 1

In functions; translations are used to move lines, points or shapes across the graph (i.e. up, down, right or left).

The translation from $y = (x - 5)^2 +5$ to $y = (x - 0)^2 +0$ is to shift $y = (x - 5)^2 +5$ to the left by 5 units and then downward by 5 units

The given parameters are:

$y = (x - 5)^2 +5$

$y = (x - 0)^2 +0$

Assume the first point is: $y = (x - 5)^2 +5$

While the second is: $y = (x - 0)^2 +0$

The first point is first shifted left by 5 units

The rule to this translation is: $(x,y) \to (x + 5,y)$

So, we have:

$y' = (x - 5 + 5)^2 + 5$

$y' = (x - 0)^2 + 5$

Next, the resulting function is shifted down by 5 units.

The rule to this translation is: $(x,y) \to (x,y- 5)$

So, we have:

$y" = y' - 5$

This gives:

$y" = (x - 0)^2 + 5 - 5$

$y" = (x - 0)^2 + 0$

Hence, the translation from $y = (x - 5)^2 +5$ to $y = (x - 0)^2 +0$ is to shift $y = (x - 5)^2 +5$ to the left by 5 units and then downward by 5 units

Read more about transformations at:

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