# Question Video: Sketching the Graph of a Quadratic Function Using a Table Mathematics

Sketch the graph of the quadratic function π(π₯) = π₯Β² β 1 on the domain interval the closed interval [β2, 2] by completing the table.

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### Video Transcript

Sketch the graph of the quadratic function π of π₯ equals π₯ squared minus one on the domain interval the closed interval from negative two to two by completing the following table.

Weβve been instructed to complete the sketch by using this table. Our first step is then to plug in each of these five values for π₯ and find the output value. First, π of negative two equals negative two squared minus one, which is three. And then π of negative one equals negative one squared minus one, which is zero. π of zero equals zero squared minus one, which is negative one. π of one, one squared minus one equals zero. π of two equals two squared minus one, which is three.

Now letβs clear some space and think about what graphing quadratic function is like. First of all, we recall that a quadratic function has the shape called a parabola that opens either upward or downward. For a quadratic in standard form π of π₯ equals ππ₯ squared plus ππ₯ plus π, if π is greater than zero for π is positive, the parabola will open upward. If π is negative, the parabola will open downward. In our case, π of π₯ equals π₯ squared minus one. Our π-value is one; itβs greater than zero. So our sketch will open upward.

Looking at our table, weβre dealing with π₯-values from negative two to two. And we know that this function is on the closed interval negative two to two. Our π of π₯ values range from negative one to three. A sensible scale might look something like this for the π₯- and π¦-axis. Weβll work on our sketch by first plotting the points from our table: negative two, three; negative one, zero; zero, negative one; one, zero; and two, three. As weβve already recognized, this parabola opens upward. Between these points, we sketch the shape of a parabola. Notice here that the parabola is symmetrical about the point zero, negative one.

We can see that that is the vertex as there is a symmetry about that point, both in our table and on the graph. Note here that as this is a closed domain, negative two, three and two, three are endpoints of this function. We wouldnβt extend the graph further past negative two or two. To find this sketch, we plotted points from a table and then connected these points with a smooth curve, which gives us a sketch of the function π of π₯ equals π₯ squared minus one on the domain interval negative two, two.