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Exercises Systems of equations

Example 4 from Algebra and Trigonometry, 11.3 Systems of Nonlinear Equations and Inequalities: Two Variables

Graphing an Inequality for a Parabola

Graph the inequality $y > x^{2} + 1.$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
First, graph the corresponding equation $y = x^{2} + 1.$ Since $y > x^{2} + 1$ has a greater than symbol, we draw the graph with a dashed line. Then we choose points to test both inside and outside the parabola. Let’s test the points
$(0, 2)$ and $(2, 0) .$ One point is clearly inside the parabola and the other point is clearly outside.
$\begin{array}{l} y > x^{2} + 1 \\ 2 > {(0)}^{2} + 1 \\ 2 > 1 & True \\ 0 > {(2)}^{2} + 1 \\ 0 > 5 & False \end{array}$
The graph is shown in Figure 9. We can see that the solution set consists of all points inside the parabola, but not on the graph itself.

Figure 9

How did it go?

PreviousSolving a System of Nonlinear Equations Representing a Circle and an Ellipse Next Graphing a System of Inequalities

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 11.3, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.