Question Video: Using a Table of Values Identify the Correct Graph of a Quadratic Function Mathematics • Third Year of Preparatory School

Video Transcript

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

We’ve been given specific instructions about the way we’re to choose the correct graph, and that’s to use the table. In the table, we’re given five different 𝑥-values. And we’ll use these five values to find the respective 𝑓 of 𝑥 values for that 𝑥. First, we have 𝑓 of negative two equals negative negative two squared plus one. Be careful that the negative two is what we’re squaring, and then we’re taking the negative of 𝑥 squared. Negative two squared is four, which means we’ll have negative four plus one.

Therefore, 𝑓 of negative two equals negative three. 𝑓 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. 𝑓 of zero equals negative zero squared plus one, which equals one. 𝑓 of one equals zero. And 𝑓 of two equals negative three.

Let’s 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 𝑓 of 𝑥 equals negative 𝑥 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 𝑓 of 𝑥 equals negative 𝑥 squared plus one is identified by the graph (C).