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PLEASEE SHOW WORK AND PLEASEE WRITE NEATLY

PLEASEE SHOW WORK AND PLEASEE WRITE NEATLY

Algebra and Trigonometry (6th Edition)
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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PLEASEE SHOW WORK AND PLEASEE WRITE NEATLY
### Instructions for Students **Question a:** On the set of axes below, draw the graph of \( y = x^2 - 4x - 1 \). **Explanation:** - There is a blank Cartesian coordinate system provided with the given question. The axes are labeled as \( x \) (horizontal axis) and \( y \) (vertical axis). - The horizontal and vertical lines form a grid. Each grid line represents one unit. To draw the graph of the function \( y = x^2 - 4x - 1 \): 1. Calculate the value of \( y \) for various values of \( x \), for example, \( x = -2, -1, 0, 1, 2, 3, 4 \). 2. Plot the calculated points on the provided coordinate grid. 3. Connect the points smoothly to form a parabolic curve that opens upwards since the coefficient of \( x^2 \) is positive. Mathematically, you could start by identifying special points such as: - The vertex of the parabola, - The y-intercept (when \( x = 0 \) → \( y = -1 \)), - The x-intercepts (where the graph crosses the x-axis). **Question b:** State the **equation** of the axis of symmetry. _____________________________ **Explanation:** - The axis of symmetry of a parabola given by \( y = ax^2 + bx + c \) has the equation \( x = -\frac{b}{2a} \). - For the given equation \( y = x^2 - 4x - 1 \), \( a = 1 \), \( b = -4 \). - Calculate the axis of symmetry: \( x = -\frac{-4}{2 \cdot 1} = 2 \). Hence, the equation of the axis of symmetry is \( x = 2 \). --- This explanation aims to provide students with a clear and step-by-step approach to solving the given problems involving quadratic functions and their graphs. Having this explanation on an educational website helps reinforce the concepts of graphing parabolas and finding their axes of symmetry.
Transcribed Image Text:### Instructions for Students **Question a:** On the set of axes below, draw the graph of \( y = x^2 - 4x - 1 \). **Explanation:** - There is a blank Cartesian coordinate system provided with the given question. The axes are labeled as \( x \) (horizontal axis) and \( y \) (vertical axis). - The horizontal and vertical lines form a grid. Each grid line represents one unit. To draw the graph of the function \( y = x^2 - 4x - 1 \): 1. Calculate the value of \( y \) for various values of \( x \), for example, \( x = -2, -1, 0, 1, 2, 3, 4 \). 2. Plot the calculated points on the provided coordinate grid. 3. Connect the points smoothly to form a parabolic curve that opens upwards since the coefficient of \( x^2 \) is positive. Mathematically, you could start by identifying special points such as: - The vertex of the parabola, - The y-intercept (when \( x = 0 \) → \( y = -1 \)), - The x-intercepts (where the graph crosses the x-axis). **Question b:** State the **equation** of the axis of symmetry. _____________________________ **Explanation:** - The axis of symmetry of a parabola given by \( y = ax^2 + bx + c \) has the equation \( x = -\frac{b}{2a} \). - For the given equation \( y = x^2 - 4x - 1 \), \( a = 1 \), \( b = -4 \). - Calculate the axis of symmetry: \( x = -\frac{-4}{2 \cdot 1} = 2 \). Hence, the equation of the axis of symmetry is \( x = 2 \). --- This explanation aims to provide students with a clear and step-by-step approach to solving the given problems involving quadratic functions and their graphs. Having this explanation on an educational website helps reinforce the concepts of graphing parabolas and finding their axes of symmetry.
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