Question

If f(x) = x2, which of the following describes the graph of f(x) - 5? A)The graph of f(x) - 5 is a vertical shift of f(x) = x2 five units up. B)The graph of f(x) - 5 is a vertical shift of f(x) = x2 five units down. C)The graph of f(x) - 5 is a horizontal shift of f(x) = x2 five units to the right. D)The graph of f(x) - 5 is a horizontal shift of f(x) = x2 five units to the left.

Answer 1

f(x) = x^2 is a parabola with vertex at the origin (0,0).
f(x) = x^2 - 5 is a parabola shifted down 5 units so it's vertex would be at (0, -5)
The correct answer is Letter B

Answer 2

Option B The graph of
`f(x)-5` is a vertical shift of
`f(x)=x^(2)` five units down.

Explanation:

we have

`f(x)=x^(2)`

Is a vertical parabola open upward with the vertex at
`(0,0)`

Let

`g(x)=f(x)-5`

so

`g(x)=x^(2)-5`

Is a vertical parabola open upward with the vertex at
`(0,-5)`

The rule of the translation of f(x)-----> g(x) is equal to

`(x,y)------> (x.y-5)`

That means-----> The translation is
`5` units down

therefore

The graph of
`f(x)-5` is a vertical shift of
`f(x)=x^(2)` five units down.