Question

Use the image to answer the question.

Two parabolas and two inverted parabolas, all with arrows on both ends, are drawn on a coordinate plane with the x-axis from negative 6 to 6 and the y-axis from negative 6 to 6, both in increments of 1.
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The two parabolas lie in the second and first quadrants, while the two inverse parabolas lie in the third and fourth quadrants. The first parabola is labeled f left parenthesis x right parenthesis equals left parenthesis x plus 3 close parenthesis superscript 2 baseline and passes through left parenthesis negative 5 comma 4 right parenthesis, has the vertex at left parenthesis negative 3 comma 0 right parenthesis, and continues through left parenthesis negative 1 comma 4 right parenthesis. The second parabola is labeled option 1 and passes through left parenthesis 0 comma 4 right parenthesis, has the vertex at left parenthesis 2 comma 0 right parenthesis, and continues through left parenthesis 4 comma 4 right parenthesis. The first inverse parabola is labeled option 2 and passes through left parenthesis negative 5 comma negative 4 right parenthesis, has the vertex at left parenthesis negative 3 comma 0 right parenthesis, and continues through left parenthesis negative 1 comma negative 4 right parenthesis. The second inverse parabola is labeled option 3 and passes through left parenthesis 0 comma negative 4 right parenthesis, has the vertex at left parenthesis 2 comma 0 right parenthesis, and continues through left parenthesis 4 comma negative 4 right parenthesis.

Given the graph of f(x)=(x+3)2
, which of the options is the graph of y=−f(x)
?

(1 point)
The graph of y=−f(x)
is option
.

Answer 1

The graph is option 2 — it is the parabola y = −(x+3)^2 with vertex at (−3,0) and points (−5,−4), (−1,−4).