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

Answer:

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

Step-by-step 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.