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Ch. 1 - Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 1 - Equations and InequalitiesProblem 25a
Chapter 2, Problem 25a

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = 9 - x2

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1
Step 1: Understand the equation. The given equation is y = 9 - x^2. This is a quadratic equation, and its graph will be a parabola. The term -x^2 indicates that the parabola opens downward because the coefficient of x^2 is negative.
Step 2: Create a table of values. Substitute the given x-values (-3, -2, -1, 0, 1, 2, 3) into the equation y = 9 - x^2 to calculate the corresponding y-values. For example, when x = -3, y = 9 - (-3)^2 = 9 - 9 = 0. Repeat this process for all x-values.
Step 3: Plot the points. Once you have the table of values, plot the points (x, y) on a coordinate plane. For example, if x = -3 gives y = 0, plot the point (-3, 0). Repeat for all other x-values.
Step 4: Draw the graph. After plotting all the points, connect them smoothly to form the parabola. Ensure the curve is symmetric about the y-axis, as the equation y = 9 - x^2 is symmetric with respect to the y-axis.
Step 5: Analyze the graph. The vertex of the parabola is at (0, 9), which is the maximum point since the parabola opens downward. The x-intercepts are the points where y = 0, and the y-intercept is the point where x = 0. Verify these features on your graph.

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Key Concepts

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

Quadratic Functions

A quadratic function is a polynomial function of degree two, typically expressed in the form y = ax^2 + bx + c. The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of 'a'. Understanding the shape and properties of parabolas is essential for graphing equations like y = 9 - x^2.
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Vertex of a Parabola

The vertex of a parabola is the highest or lowest point on its graph, depending on its orientation. For the equation y = 9 - x^2, the vertex is at the point (0, 9), which is the maximum value of y. Identifying the vertex helps in sketching the graph accurately and understanding the function's behavior.
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Graphing Points

Graphing points involves plotting specific values of x and their corresponding y values on a coordinate plane. In this case, substituting x values from -3 to 3 into the equation y = 9 - x^2 allows us to find the corresponding y values, which are then plotted to visualize the parabola. This process is crucial for accurately representing the function's graph.
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Related Practice
Textbook Question

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Solve each equation in Exercises 15–34 by the square root property. (x−3)2=−5(x - 3)^2 = - 5

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