Respuesta :

mathstudent55

Answer:

See below.

Step-by-step explanation:

Equation of parabola:

y = some expression in x^2

To translate the parabola vertically, substitute y with y - k.

The translation is k units vertically. If k is positive, the translation is up. If k is negative the translation is down.

Example 1:

original parabola: y = x^2 - 2x + 5

To translate it 3 units up, we need k = 3.

Substitute y with y - 5 to get

y - 3 = x^2 - 2x + 5

y = x^2 - 2x + 8 is the equation of the parabola translated 3 units up.

Example 2:

original parabola: y = 2x^2 + 4x - 6

To translate it 5 units down, we need k = -5.

Substitute y with y - (-5), or y = 5 to get

y + 5 = 2x^2 + 4x - 6

y = 2x^2 + 4x - 11

y = 2x^2 + 4x - 11 is the equation of the parabola translated 5 units down.

facundo3141592

A vertical translation of N units applied to the general parabola gives:

y = a*x^2 + b*x + (c + N).

How to translate a parabola vertically?

For a general function f(x), we define a vertical translation of N units as:

g(x) = f(x) + N.

  • If N is positive, the translation is upwards.
  • If N is negative, the translation is downwards.

So, for a general parabola:

y = a*x^2 + b*x + c

A translation of N units is just written as:

y' = a*x^2 + b*x + (c + N).

That is how to change the equation of the parabola to translate it vertically.

If you want to learn more about parabolas, you can read:

https://brainly.com/question/1214333

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