Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 + 2x + 6? left 1 unit, up 5 units right 1 unit, up 5 units left 2 units, up 2 units right 2 units, up 2 units

left 1 unit, up 5 units

Step-by-step explanation:

First, rewrite the function as

Note that

Hence, the function is translated 1 unit to the left and 5 units up function

Option 1. Shifting of 5 units up and 1 unit left.

Step-by-step explanation:

If we draw a function graphically y = x² and then it is translated onto g(x) = x²+2x+6. Then we get to know that in function y = x² then its vertex is (0,0).

The second function g(x) = x²+2x+6 can be represented in the form of equation y = x²+2x+6 of a parabola

As we know in a parabola y = ax²+bx+c,vertex (x,y) can be calculated as

x of vertex = -b/2a

From the given equation x of vertex = -2/2 = -1

and y = (-1)²+2(-1)+6 = 5

So vertex is (-1, 5). Therefore there is a shifting of 5 units up and 1 unit left to get the vertex from (0,0) to (-1,5).

addition

step-by-step explanation: