Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
Factor the following expression completely. Please show all work.
![### Quadratic Expression
Consider the quadratic expression:
\[ 5x^2 - 45x + 100 \]
This expression is a standard form of a quadratic equation, represented as \( ax^2 + bx + c \), where:
- \( a = 5 \) (the coefficient of \( x^2 \))
- \( b = -45 \) (the coefficient of \( x \))
- \( c = 100 \) (the constant term)
#### Understanding the Components:
- **Quadratic Term (\( 5x^2 \))**: This term represents the parabolic shape of the graph when plotted. It determines the direction and width of the parabola.
- **Linear Term (\( -45x \))**: This term affects the slope or tilt of the graph, shifting the vertex of the parabola horizontally.
- **Constant Term (\( +100 \))**: This value shifts the entire graph vertically on the y-axis.
Understanding these components is crucial for solving, graphing, and analyzing quadratic equations in various mathematical problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffa90148-adb6-484b-b43e-a7e63583a4db%2Fd854ca9d-7843-4055-8c6e-59e873432974%2Fwcj5rj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Quadratic Expression
Consider the quadratic expression:
\[ 5x^2 - 45x + 100 \]
This expression is a standard form of a quadratic equation, represented as \( ax^2 + bx + c \), where:
- \( a = 5 \) (the coefficient of \( x^2 \))
- \( b = -45 \) (the coefficient of \( x \))
- \( c = 100 \) (the constant term)
#### Understanding the Components:
- **Quadratic Term (\( 5x^2 \))**: This term represents the parabolic shape of the graph when plotted. It determines the direction and width of the parabola.
- **Linear Term (\( -45x \))**: This term affects the slope or tilt of the graph, shifting the vertex of the parabola horizontally.
- **Constant Term (\( +100 \))**: This value shifts the entire graph vertically on the y-axis.
Understanding these components is crucial for solving, graphing, and analyzing quadratic equations in various mathematical problems.
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