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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![**Solving Quadratic Inequalities Using a Graph**
**Objective:** Use the graph of the quadratic function \( f \) to determine the solution.
**Tasks:**
(a) Solve \( f(x) > 0 \).
(b) Solve \( f(x) \leq 0 \).
**Explanation of the Graph:**
The graph displays a parabola opening upwards, intersecting the x-axis at two points. The x-axis and y-axis are labeled, and the scales are marked.
- **X-intercepts:** The parabola intersects the x-axis at approximately \( x = -5 \) and \( x = 5 \).
- **Vertex:** The lowest point of the parabola, located at the midpoint of the intercepts.
**Interval Notation for Solutions:**
- **(a) The solution to \( f(x) > 0 \) is:**
Values of \( x \) where the graph is above the x-axis, which is \( (-\infty, -5) \cup (5, \infty) \).
- **(b) The solution to \( f(x) \leq 0 \) is:**
Values of \( x \) on or below the x-axis, which is \( [-5, 5] \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F236445ec-9d0f-4c35-9ff5-c25a947921c3%2F4bdba097-bda3-49e6-929c-1a490432ce56%2Fpdk94i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solving Quadratic Inequalities Using a Graph**
**Objective:** Use the graph of the quadratic function \( f \) to determine the solution.
**Tasks:**
(a) Solve \( f(x) > 0 \).
(b) Solve \( f(x) \leq 0 \).
**Explanation of the Graph:**
The graph displays a parabola opening upwards, intersecting the x-axis at two points. The x-axis and y-axis are labeled, and the scales are marked.
- **X-intercepts:** The parabola intersects the x-axis at approximately \( x = -5 \) and \( x = 5 \).
- **Vertex:** The lowest point of the parabola, located at the midpoint of the intercepts.
**Interval Notation for Solutions:**
- **(a) The solution to \( f(x) > 0 \) is:**
Values of \( x \) where the graph is above the x-axis, which is \( (-\infty, -5) \cup (5, \infty) \).
- **(b) The solution to \( f(x) \leq 0 \) is:**
Values of \( x \) on or below the x-axis, which is \( [-5, 5] \).
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