Textbook Question
Multiply or divide, as indicated. See Example 3. (15p³ / 9p²) • (12p / 10p³)
7
views
Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 1, Problem 33
For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4.
y = x²
Verified step by step guidance1
Step 1: Understand the equation given, which is \(y = x^{2}\). This is a quadratic function where \(y\) is the square of \(x\). The graph of this equation is a parabola opening upwards.
Step 2: To create a table of ordered pairs, choose at least three values for \(x\). For example, select \(x = -1\), \(x = 0\), and \(x = 1\).
Step 3: Calculate the corresponding \(y\) values by substituting each \(x\) into the equation \(y = x^{2}\). For \(x = -1\), compute \(y = (-1)^{2}\); for \(x = 0\), compute \(y = 0^{2}\); and for \(x = 1\), compute \(y = 1^{2}\).
Step 4: Write the ordered pairs as \((x, y)\) using the values found in Step 3. These pairs will be points on the graph of the equation.
Step 5: To graph the equation, plot the ordered pairs on the coordinate plane and draw a smooth curve through these points forming a parabola opening upwards. You can also choose additional \(x\) values to get more points for a more accurate graph.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
5mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Understanding the Equation y = x²
The equation y = x² represents a quadratic function where the output y is the square of the input x. This creates a parabola opening upwards, symmetric about the y-axis. Recognizing this form helps in predicting the shape and behavior of the graph.
Recommended video:
04:47
Introduction to Parametric Equations
Creating Ordered Pairs from an Equation
To find ordered pairs (x, y) that satisfy y = x², select values for x and compute y by squaring x. This process generates points on the graph, which can be tabulated to visualize the function's behavior and assist in plotting.
Recommended video:
6:50Convert Equations from Polar to Rectangular
Graphing Quadratic Functions
Graphing y = x² involves plotting the ordered pairs on a coordinate plane and connecting them smoothly to form a parabola. Understanding key features like the vertex at (0,0) and symmetry helps in accurately sketching the curve.
Recommended video:
6:36Quadratic Formula
Related Practice
Textbook Question
Let A = {-6, -12⁄4, -5⁄8, -√3, 0, ¼, 1, 2π, 3, √12}. List all the elements of A that belong to each set. Rational numbers
Textbook Question
Find the square of each radical expression. See Example 2. √3x² + 4
3
views
Textbook Question
Find each sum or difference. See Example 1. -2 - |-4|
Textbook Question
Let A = {-6, -12⁄4, -5⁄8, -√3, 0, ¼, 1, 2π, 3, √12}. List all the elements of A that belong to each set. Integers
Textbook Question
Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. x = y⁶
2
views