Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
Find the zeros of the function algebraically
![### Quadratic Functions
The following quadratic functions are given for analysis:
#### a) Function Definition
\[ f(x) = x^2 + 2x - 8 \]
This function represents a standard quadratic equation where:
- The coefficient of \( x^2 \) is 1, indicating the parabola opens upwards.
- The linear coefficient is 2.
- The constant term is -8.
#### b) Function Definition
\[ f(x) = 3x^2 + 4x - 4 \]
In this function:
- The coefficient of \( x^2 \) is 3, suggesting a steeper parabola opening upwards.
- The linear coefficient is 4.
- The constant term is -4.
#### c) Function Definition
\[ f(x) = 9x^2 - 3x - 2 \]
For this equation:
- The coefficient of \( x^2 \) is 9, indicating an even steeper parabola than the previous two, opening upwards.
- The linear coefficient is -3.
- The constant term is -2.
For better understanding, it may be beneficial to graph these functions, analyze their vertices, intercepts, and the direction in which each parabola opens.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4117cac-23e7-449a-b251-99443c1e90ff%2F94cc1b1f-92e8-4714-abda-ea4831f21142%2Fm6h601_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Quadratic Functions
The following quadratic functions are given for analysis:
#### a) Function Definition
\[ f(x) = x^2 + 2x - 8 \]
This function represents a standard quadratic equation where:
- The coefficient of \( x^2 \) is 1, indicating the parabola opens upwards.
- The linear coefficient is 2.
- The constant term is -8.
#### b) Function Definition
\[ f(x) = 3x^2 + 4x - 4 \]
In this function:
- The coefficient of \( x^2 \) is 3, suggesting a steeper parabola opening upwards.
- The linear coefficient is 4.
- The constant term is -4.
#### c) Function Definition
\[ f(x) = 9x^2 - 3x - 2 \]
For this equation:
- The coefficient of \( x^2 \) is 9, indicating an even steeper parabola than the previous two, opening upwards.
- The linear coefficient is -3.
- The constant term is -2.
For better understanding, it may be beneficial to graph these functions, analyze their vertices, intercepts, and the direction in which each parabola opens.
Expert Solution
Step 1
Apply the quadratic formula to find the roots algebraically.
Step by step
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