### Video Transcript

By completing the table of values
for π of π₯ equals negative π₯ squared plus one, identify the correct graph of the
quadratic function.

Weβve been given specific
instructions about the way weβre to choose the correct graph, and thatβs to use the
table. In the table, weβre given five
different π₯-values. And weβll use these five values to
find the respective π of π₯ values for that π₯. First, we have π of negative two
equals negative negative two squared plus one. Be careful that the negative two is
what weβre squaring, and then weβre taking the negative of π₯ squared. Negative two squared is four, which
means weβll have negative four plus one.

Therefore, π of negative two equals
negative three. π of negative one will equal the
negative of negative one squared plus one. Negative one squared is one. The negative of that is negative
one plus one equals zero. π of zero equals negative zero
squared plus one, which equals one. π of one equals zero. And π of two equals negative
three.

Letβs start by graphing the point
zero, one on the graphs. By doing that, we can eliminate
(A), (B), and (D). At this point, we can notice that
our π of π₯ equals negative π₯ squared plus one, and therefore we know that this
graph is going to open downward. Additionally, if we add the points
negative one, zero and one, zero to the graph, we see that option (C) must be
correct. Using the table, we found that π
of π₯ equals negative π₯ squared plus one is identified by the graph (C).