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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- Define the function p using the function f.
- What is the function rule for p?

Transcribed Image Text:The image illustrates a graph with three quadratic functions plotted on a Cartesian coordinate grid.
1. **Function \( f(x) \)**:
- Depicted in black.
- Has a vertex at \((0, 1)\) and opens upwards.
- Symmetrical about the y-axis.
- Passes through points such as \((-3, 10)\), \((-2, 5)\), \((-1, 2)\), \((1, 2)\), \((2, 5)\), \((3, 10)\).
2. **Function \( g(x) \)**:
- Shown in blue.
- Opens upwards with a vertex at \((5, 0)\).
- Symmetrical about the line \(x = 5\).
- Passes through points such as \((3, 4)\), \((4, 1)\), \((6, 1)\), \((7, 4)\).
3. **Function \( h(x) \)** and **Function \( p(x) \)**:
- Function \( h(x) \) is in red, and Function \( p(x) \) is in green.
- Both have vertices close to \((4, 0)\) and open upwards.
- They trace closely but are not identical, with \( h(x) \) slightly broader than \( p(x) \).
- The vertex of \( h(x) \) is at \((4,1)\) and it runs above \( p(x)\).
The grid lines indicate integer values on the x-axis from \(-3\) to \(8\) and on the y-axis from \(1\) to \(11\). The functions illustrate different parabolic shapes and transformations compared to the basic function \( f(x) \).
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