Graph. Label Vertex, LOS, intercepts f(x) = - (x + 2)² + 5
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Question
![**Graphing a Quadratic Function**
**Objective:**
Graph the quadratic function. Label the Vertex, Line of Symmetry (LOS), and intercepts.
**Function:**
\[ f(x) = -(x + 2)^2 + 5 \]
**Steps:**
1. **Identify the Vertex:**
- The function is in vertex form \[ f(x) = a(x-h)^2 + k \].
- Here, \( a = -1 \), \( h = -2 \), \( k = 5 \).
- Vertex: \((-2, 5)\)
2. **Line of Symmetry (LOS):**
- The line of symmetry is the vertical line that passes through the vertex.
- Equation: \( x = -2 \).
3. **Intercepts:**
- **y-intercept:** Set \( x = 0 \).
\[ f(0) = -(0 + 2)^2 + 5 \]
\[ f(0) = -4 + 5 = 1 \]
- y-intercept: \((0, 1)\)
- **x-intercepts:** Set \( f(x) = 0 \).
\[ 0 = -(x + 2)^2 + 5 \]
\[ -(x + 2)^2 = -5 \]
\[ (x + 2)^2 = 5 \]
\[ x + 2 = ±\sqrt{5} \]
\[ x = -2 ± \sqrt{5} \]
**Graph Description:**
- The graph is a downward-opening parabola due to the negative coefficient (\( a = -1 \)).
- The vertex \((-2, 5)\) is the highest point on the graph.
- The LOS is at \( x = -2 \).
- The parabola crosses the y-axis at \( (0, 1) \).
- The x-intercepts are located at \((-2 + \sqrt{5}, 0)\) and \((-2 - \sqrt{5}, 0)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F068b423d-81fb-41c7-8616-9d34c4d0769a%2F3bdf4547-e081-41ca-844a-8b9fd5095cdd%2Fu6xdq3a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graphing a Quadratic Function**
**Objective:**
Graph the quadratic function. Label the Vertex, Line of Symmetry (LOS), and intercepts.
**Function:**
\[ f(x) = -(x + 2)^2 + 5 \]
**Steps:**
1. **Identify the Vertex:**
- The function is in vertex form \[ f(x) = a(x-h)^2 + k \].
- Here, \( a = -1 \), \( h = -2 \), \( k = 5 \).
- Vertex: \((-2, 5)\)
2. **Line of Symmetry (LOS):**
- The line of symmetry is the vertical line that passes through the vertex.
- Equation: \( x = -2 \).
3. **Intercepts:**
- **y-intercept:** Set \( x = 0 \).
\[ f(0) = -(0 + 2)^2 + 5 \]
\[ f(0) = -4 + 5 = 1 \]
- y-intercept: \((0, 1)\)
- **x-intercepts:** Set \( f(x) = 0 \).
\[ 0 = -(x + 2)^2 + 5 \]
\[ -(x + 2)^2 = -5 \]
\[ (x + 2)^2 = 5 \]
\[ x + 2 = ±\sqrt{5} \]
\[ x = -2 ± \sqrt{5} \]
**Graph Description:**
- The graph is a downward-opening parabola due to the negative coefficient (\( a = -1 \)).
- The vertex \((-2, 5)\) is the highest point on the graph.
- The LOS is at \( x = -2 \).
- The parabola crosses the y-axis at \( (0, 1) \).
- The x-intercepts are located at \((-2 + \sqrt{5}, 0)\) and \((-2 - \sqrt{5}, 0)\).
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