Question

The parabola descends and then rises in quadrant 2. The curve starts passes through left parenthesis negative 3.6 comma 5 right parenthesis, left parenthesis negative 3 comma 2 right parenthesis, has a valley at left parenthesis negative 2 comma 0 right parenthesis, rises through left parenthesis negative 1 comma 2 right parenthesis, and left parenthesis negative 0.4 comma 5 right parenthesis. All values are approximate.


The graph of a transformed function is shown. Determine the parent function and the equation of the transformed function.

(1 point)
Responses

The parent function is y=(x+2)2
. The equation of the transformed function is y=x2
.
The parent f unction is y is equal to open paren x plus 2 close paren squared. The equation of the transformed function is y is equal to x squared.

The parent function is y=x2
. The equation of the transformed function is y=(x−2)2
.
The parent function is y is equal to x squared. The equation of the transformed function is y is equal to open paren x minus 2 close paren squared.

The parent function is y=(x−2)2
. The equation of the transformed function is y=x2
.
The parent f unction is y is equal to open paren x minus 2 close paren squared. The equation of the transformed function is y is equal to x squared.

The parent function is y=x2
. The equation of the transformed function is y=(x+2)2
.
The parent function is y is equal to x squared. The equation of the transformed function is y is equal to open paren x plus 2 close paren squared.

Answer 1

Parent function: y = x^2.

Transformed function: y = 2(x + 2)^2.

Reason: vertex at (-2,0) → shift left 2 so y = a(x+2)^2. Using (-3,2): 2 = a(-1)^2 ⇒ a = 2, so y = 2(x+2)^2 (this also matches the other sample points approximately).