The graphs below have the same shape. What is the equation of the blue

Mathematics

1 answer:

PIT_PIT [12.4K]2 months ago

4 0

Answer:

Answer choice C. $g(x)=(x+3)^2+1$ .

Step-by-step explanation:

The entire question is present in the attached figure.

It is established that

The function f(x) is represented by

$f(x)=x^2$ ,

indicating a parabola that opens upward.

The vertex is situated at the point (0,0).

The function g(x) shares the same parabolic shape.

The vertex of g(x) is located at (-3,1).

Therefore,

The transformation from f(x) to g(x) can be described as:

(0,0) transforms to (-3,1).

(x,y) transforms to (x-3,y+1).

This indicates a shift of 3 units to the left and 1 unit upward.

Thus,

The equation for g(x) in vertex form can be expressed as

$g(x)=(x+3)^2+1$ .

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