Question

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 + 2x +1?

Answer 1

Answer:

Option B is correct

Left 1 unit.

Explanation:

According to the graph theory of transformation:

y = f(x+k)=$\left \{ {{k>0 shift graph of y= f(x) left k unit} \atop {k$

Given the parent function: $f(x)=x^2$

and the function $g(x)=x^2+2x+1$

we can write it as:

g(x)= $(x+1)^2$   [ ∴$(a+b)^2 = a^2+2ab+b^2$ ]

Therefore, vertex of the graph of the function $g(x)=(x+1)^2$ is 1 units to the left of the vertex of the graph of the function $f(x)=x^2$ .

Answer 2

Answer:

Shift 1 unit left

B is correct

Step-by-step explanation:

Given: The vertex of f(x) shift to g(x)

$f(x)=x^2$

Vertex of f(x): (0,0)

$g(x)=x^2+2x+1$

Vertex form: $y=a(x-h)^2+k$

$g(x)=(x+1)^2$

Vertex of g(x): (-1,0)

$(0,0)\rightarrow (-1,0)$

Only x-coordinate change and y-coordinate remain same.

$0\rightarrow -1$

Hence, The vertex of f(x) shift 1 unit left to get vertex of g(x)