Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Question
**Quadratic Functions and Their Properties** **Consider the function \( f(x) = x^2 + 6x + 4 \)** 1. **What is the vertex of \( f \)?** \[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_ \] 2. **What is the equation of the line of symmetry of \( f \)?** \[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_ \] 3. **\( f \) has a** \[ \text{(Select an answer)} \] **of** \[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_ \] \[ \text{(Dropdown options:} \: \text{maximum, minimum)} \] 4. **The \( x \)-intercept(s) of \( f(x) \) are** \[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_ \] 5. **The \( y \)-intercept of \( f \) is** \[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_ \] --- ### Graph \( f(x) \) To the right of the questions, there is a graph of the function \( f(x) \) on a coordinate plane. This plane has the \( x \)-axis ranging from -10 to 10 and the \( y \)-axis ranging from -10 to 10. The graph is divided into a grid with major gridlines representing integer values on both axes. Below the graph, there are tools for drawing: 1. A straight line tool. 2. A parabolic curve tool. 3. An exponential decay or growth curve tool. 4. A circle or ellipse tool. These tools can be used to visualize the function \( f(x) \) and its key properties such as intercepts, vertex, and symmetry.
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Transcribed Image Text:**Quadratic Functions and Their Properties** **Consider the function \( f(x) = x^2 + 6x + 4 \)** 1. **What is the vertex of \( f \)?** \[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_ \] 2. **What is the equation of the line of symmetry of \( f \)?** \[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_ \] 3. **\( f \) has a** \[ \text{(Select an answer)} \] **of** \[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_ \] \[ \text{(Dropdown options:} \: \text{maximum, minimum)} \] 4. **The \( x \)-intercept(s) of \( f(x) \) are** \[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_ \] 5. **The \( y \)-intercept of \( f \) is** \[ \_\_\_\_\_\_\_\_\_\_\_\_\_\_ \] --- ### Graph \( f(x) \) To the right of the questions, there is a graph of the function \( f(x) \) on a coordinate plane. This plane has the \( x \)-axis ranging from -10 to 10 and the \( y \)-axis ranging from -10 to 10. The graph is divided into a grid with major gridlines representing integer values on both axes. Below the graph, there are tools for drawing: 1. A straight line tool. 2. A parabolic curve tool. 3. An exponential decay or growth curve tool. 4. A circle or ellipse tool. These tools can be used to visualize the function \( f(x) \) and its key properties such as intercepts, vertex, and symmetry.
### Quadratic Function Analysis Consider the function \( f(x) = x^2 + 6x + 4 \). 1. **Vertex of \( f \)**: - What is the vertex of \( f \)? - [Input Box for Answer] 2. **Line of Symmetry**: - What is the equation of the line of symmetry of \( f \)? - [Input Box for Answer] 3. **Nature of Vertex**: - \( f \) has a [Dropdown Menu] of - Options could include minimum, maximum, etc. 4. **\( x \)-intercepts**: - The \( x \)-intercept(s) of \( f \) is/are - [Input Box for Answer] 5. **\( y \)-intercept**: - The \( y \)-intercept of \( f \) is - [Input Box for Answer] ### Graph of \( f(x) \) To the right, there is a coordinate plane graph illustrating the quadratic function \( f(x) \) with axes intersecting at (\(0,0\)). The graph extends from -10 to 10 on both the x-axis and y-axis. #### Features of the Graph: - **Coordinate Plane**: The plane is marked with grid lines for accurate plotting, with every 1 unit increment marked on both axes. - **Graph Tools**: Below the graph, there are options to draw or plot points including: - A dot - A line - A parabola - A line segment - A circle There are also options to "Clear All" which likely removes all plots or drawings from the graph. This exercise aims to understand the components and characteristics of the quadratic function, specifically focusing on vertex, symmetry, intercepts, and graphical representation.
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Transcribed Image Text:### Quadratic Function Analysis Consider the function \( f(x) = x^2 + 6x + 4 \). 1. **Vertex of \( f \)**: - What is the vertex of \( f \)? - [Input Box for Answer] 2. **Line of Symmetry**: - What is the equation of the line of symmetry of \( f \)? - [Input Box for Answer] 3. **Nature of Vertex**: - \( f \) has a [Dropdown Menu] of - Options could include minimum, maximum, etc. 4. **\( x \)-intercepts**: - The \( x \)-intercept(s) of \( f \) is/are - [Input Box for Answer] 5. **\( y \)-intercept**: - The \( y \)-intercept of \( f \) is - [Input Box for Answer] ### Graph of \( f(x) \) To the right, there is a coordinate plane graph illustrating the quadratic function \( f(x) \) with axes intersecting at (\(0,0\)). The graph extends from -10 to 10 on both the x-axis and y-axis. #### Features of the Graph: - **Coordinate Plane**: The plane is marked with grid lines for accurate plotting, with every 1 unit increment marked on both axes. - **Graph Tools**: Below the graph, there are options to draw or plot points including: - A dot - A line - A parabola - A line segment - A circle There are also options to "Clear All" which likely removes all plots or drawings from the graph. This exercise aims to understand the components and characteristics of the quadratic function, specifically focusing on vertex, symmetry, intercepts, and graphical representation.
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Step 2: Vertex
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Step 3: Equation of the line of symmetry, minimum value
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Step 4: x,y-intercepts
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