Skip to main content
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

Verified step by step guidance
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.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
3m
Was this helpful?

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.
Recommended video:
06:36
Solving Quadratic Equations Using The Quadratic Formula

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.
Recommended video:
5:28
Horizontal Parabolas

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.
Recommended video:
Guided course
04:29
Graphing Equations of Two Variables by Plotting Points
Related Practice
Textbook Question

Solve and check each linear equation. 25 - [2 + 5y - 3(y + 2)] = - 3(2y - 5) - [5(y - 1) - 3y + 3]

913
views
1
rank
Textbook Question

Divide and express the result in standard form. - 6i/(3 + 2i)

869
views
Textbook Question

In Exercises 15–26, use graphs to find each set. [3, ∞) ⋃ (6, ∞)

772
views
Textbook Question

A rectangular swimming pool is three times as long as it is wide. If the perimeter of the pool is 320 feet, what are its dimensions?

692
views
Textbook Question

Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(2x + 3) + √(x - 2) = 2

787
views
Textbook Question

A rectangular soccer field is twice as long as it is wide. If the perimeter of the soccer field is 300 yards, what are its dimensions?

691
views