Question

Use the graph to answer the question.

A parabola is drawn on a coordinate plane. Both axes range from negative 5 to 5 in one-unit increments.
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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)

The parent function is y=(x−2)2
. The equation of the transformed function is y=x2
.

The parent function is y=(x+2)2
. The equation of the transformed function is y=x2
.

The parent function is y=x2
. The equation of the transformed function is y=(x+2)2
.

The parent function is y=x2
. The equation of the transformed function is y=(x−2)2
.

Answer 1

Parent function: y = x^2

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

Reason: The vertex is at (-2, 0), so the parabola is the graph of y = (x - (-2))^2 = (x + 2)^2 (a left shift by 2).