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

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!

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DelcieRiveria DelcieRiveria · Answer 2 · 2019-06-11T11:02:33+02:00

Answer:

The correct option is C.

Step-by-step explanation:

The parent function is

[tex]f(x)=x^2[/tex]

The translation is defined as

[tex]f(x)=(x+a)^2+b[/tex] .... (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).

[tex]f(x)=(x+(-3))^2+4[/tex]

[tex]f(x)=(x-3)^2+4[/tex]

The required rule is [tex]f(x)=(x-3)^2+4[/tex].

Therefore the correct option is C.