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Ch. 5 - Systems and Matrices
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 5 - Systems and MatricesProblem 23
Chapter 6, Problem 23

Graph each inequality. y > (x - 1)2 + 2

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Identify the boundary curve by rewriting the inequality as an equation: \(y = (x - 1)^{2} + 2\). This is a parabola opening upwards with vertex at \((1, 2)\).
Graph the parabola \(y = (x - 1)^{2} + 2\) on the coordinate plane. Since the inequality is strict ($>$), draw the parabola as a dashed curve to indicate points on the curve are not included.
Determine which side of the parabola to shade by testing a point not on the curve, such as the point \((1, 3)\). Substitute into the inequality: \(3 > (1 - 1)^{2} + 2\) simplifies to \(3 > 2\), which is true.
Since the test point satisfies the inequality, shade the region above the parabola where \(y\) values are greater than \((x - 1)^{2} + 2\).
Label the graph clearly, showing the dashed parabola and the shaded region above it to represent all solutions to the inequality \(y > (x - 1)^{2} + 2\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Graphing Quadratic Functions

A quadratic function is represented by an equation of the form y = ax² + bx + c, producing a parabola when graphed. Understanding the shape and vertex of the parabola y = (x - 1)² + 2 helps in visualizing the boundary curve for the inequality.
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Graphs of Logarithmic Functions

Inequalities and Their Graphs

Graphing inequalities involves shading the region of the coordinate plane where the inequality holds true. For y > (x - 1)² + 2, the area above the parabola is shaded, indicating all points where y-values are greater than the quadratic expression.
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Linear Inequalities

Boundary Lines and Open/Closed Curves

The boundary of the inequality y > (x - 1)² + 2 is the parabola y = (x - 1)² + 2. Since the inequality is strict (greater than, not greater than or equal to), the boundary curve is drawn as a dashed line to show points on the curve are not included in the solution.
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The Slope of a Line
Related Practice
Textbook Question

Solve each system, using the method indicated.

5x + 2y = -10

3x - 5y = -6 (Gauss-Jordan)

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Textbook Question

Evaluate each determinant.

∣120−12−1014∣\(\left\)| \(\begin{matrix}\) 1 & 2 & 0 \\ -1 & 2 & -1 \\ 0 & 1 & 4 \(\end{matrix}\) \(\right\)|

Textbook Question

Find the inverse, if it exists, for each matrix.[1010−10211]\(\left\)[ \(\begin{matrix}\) 1 & 0 & 1 \\ 0 & -1 & 0 \\ 2 & 1 & 1 \(\end{matrix}\) \(\right\)]

Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.

x2+y2=102x^2+y^2=102

x2−y2=17x^2-y^2=17

Textbook Question

Graph each inequality. x2 + (y + 3)2 ≤ 16

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Textbook Question

Use the Gauss-Jordan method to solve each system of equations. For systems in two variables with infinitely many solutions, write the solution with y arbitrary. For systems in three variables with infinitely many solutions, write the solution set with z arbitrary.

3x + 2y = -9

2x - 5y = -6

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