Identify the transformations of the graph of $f ( x ) = x ^ { 2 }$ that would produce the graph of $h ( x ) = - ( x + 3 ) ^ { 2 } + 4$ .
A)horizontal shift 3 units left; vertical shift 4 units upward
B)horizontal shift 3 units right; reflection in the x -axis; vertical shift 4 units downward
C)horizontal shift 4 units right; vertical shift 3 units downward
D)horizontal shift 4 units left; reflection in the x -axis; vertical shift 3 units upward
E)horizontal shift 3 units left; reflection in the x -axis; vertical shift 4 units upward

Question

Quizplus · Accepted Answer

The graph of $f ( x ) = x ^ { 2 }$ represents a parabola with the vertex at the origin. The negative sign in front of the expression $( x + 3 ) ^ { 2 }$ indicates that the parabola is reflected in the x-axis. The $+3$ inside the parentheses indicates a horizontal shift 3 units to the left. Finally, the $+4$ outside the parentheses indicates a vertical shift 4 units upward. Therefore, the transformation sequence is a horizontal shift 3 units left, reflection in the x-axis, and a vertical shift 4 units upward, which corresponds to answer choice E.

Identify the Transformations of the Graph Of f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2

Identify the Transformations of the Graph Of $f ( x ) = x ^ { 2 }$