Question

find the rule and the graph of the function whose graph can be obtained by preforming the translation 3 units right and 4 units up on the parent function f(x)=x^2

Answer 1

Hello!

x^2 is a parabola with a vertex of (0, 0)

Now we look for the parabola with a vertex 3 units right and 4 units up

So we are looking for a vertex of (3, 4)

So the answer is C

Hope this helps!

Answer 2

The correct option is C.

Explanation:

The parent function is

`f(x)=x^2`

The translation is defined as

`f(x)=(x+a)^2+b` .... (1)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

It is given that the quadratic function shifted 3 units right and 4 units up. It means a=-3 and b=4.

Substitute a=-3 and b=-4 in equation (1).

`f(x)=(x+(-3))^2+4`

`f(x)=(x-3)^2+4`

The required rule is
`f(x)=(x-3)^2+4`.

Therefore the correct option is C.