Question

Find g(x), where g(x) is the translation 4 units up of f(x) = x2.

Answer 1

Answer:

$g(x)=1(x-0)^{2}+4$

Step-by-step explanation:

Given:

The function,$f(x)=x^{2}$

A standard parabola with vertex at origin is represented as:

$f(x)=ax^{2}$

The above function is a standard parabola with vertex at origin and opening upward.

The vertex of the above function is at the origin $(0,0)$ and the value of $a$ is 1.

Now, the function is translated 4 units up.

So, from the rule of function transformations, if a graph is moved up by $c$ units, then $c$ units is added to the function.

Therefore,

$g(x)=f(x) + 4\\g(x)=x^{2}+4$.

Also, the vertex of $f(x)$ will be translated 4 units up. So, the co-ordinates of the vertex of $g(x)$ will be $(0,0+4)=(0,4)$

Now, express the above function in the vertex form $g(x)=a(x-h)^{2}+k$.

We have $a=1,h=0,k=4$

This gives,

$g(x)=1(x-0)^{2}+4$