Consider the following. h(t)t2 8t + 16 (a) Find all real zeros of the polynomial function. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) t = (b) Determine whether the multiplicity of each zero is even or odd. ---Select--- ✪ (c) Determine the maximum possible number of turning points of the graph of the function. turning point(s) (d) Use a graphing utility to graph the function and verify your answers. h(t) 15 10 5 V 5 10 O -15 -10 -5 -15 -10 -5 h(t) N 5E 5 15 10 10 15 -10 10 15 t t -15 -10 -15 -10 -5 -5 h(t) 15 10 -10F h(t) 15 10 -5 -10 5 5 10 10 15 15 t t
Consider the following. h(t)t2 8t + 16 (a) Find all real zeros of the polynomial function. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) t = (b) Determine whether the multiplicity of each zero is even or odd. ---Select--- ✪ (c) Determine the maximum possible number of turning points of the graph of the function. turning point(s) (d) Use a graphing utility to graph the function and verify your answers. h(t) 15 10 5 V 5 10 O -15 -10 -5 -15 -10 -5 h(t) N 5E 5 15 10 10 15 -10 10 15 t t -15 -10 -15 -10 -5 -5 h(t) 15 10 -10F h(t) 15 10 -5 -10 5 5 10 10 15 15 t t
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following.
![### Consider the following:
\[ h(t) = t^2 - 8t + 16 \]
#### (a) Find all real zeros of the polynomial function.
- *Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.*
\[ t = \underline{\hspace{3cm}} \]
#### (b) Determine whether the multiplicity of each zero is even or odd.
- *Select an option from the dropdown menu.*
\[ \text{\underline{\hspace{3cm}}}\]
#### (c) Determine the maximum possible number of turning points of the graph of the function.
- *Enter the number in the provided space.*
\[ \text{\underline{\hspace{3cm}}} \text{ turning point(s)} \]
#### (d) Use a graphing utility to graph the function and verify your answers.
### Graph Descriptions:
1. **Top Left Graph:**
- Displays the function \( h(t) \) with a vertex at \( t = 4 \), showing a parabolic shape opening upwards. The axis of symmetry appears at \( t = 4 \), and the graph crosses the y-axis near the point (0, 16).
2. **Top Right Graph:**
- Similar configuration: a parabola with upward direction. The focus seems to be around the point (4, 0), reinforcing symmetry around \( t = 4 \).
3. **Bottom Left Graph:**
- Displays a partial view of the parabola with its bottom visible, representing a vertex nearly centered at \( (4, 0) \).
4. **Bottom Right Graph:**
- A full parabola is drawn, confirming the function’s properties with a smoother curvature focused symmetrically around the line \( t = 4 \).
These graphs illustrate the characteristics of the quadratic function \( h(t) = t^2 - 8t + 16 \), helping to visualize solutions and analyze features such as turning points and symmetry.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f655a5e-3946-44a0-87d7-d06571787362%2F48f262ca-b967-40a2-9273-e25d38216641%2F22m3qy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Consider the following:
\[ h(t) = t^2 - 8t + 16 \]
#### (a) Find all real zeros of the polynomial function.
- *Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.*
\[ t = \underline{\hspace{3cm}} \]
#### (b) Determine whether the multiplicity of each zero is even or odd.
- *Select an option from the dropdown menu.*
\[ \text{\underline{\hspace{3cm}}}\]
#### (c) Determine the maximum possible number of turning points of the graph of the function.
- *Enter the number in the provided space.*
\[ \text{\underline{\hspace{3cm}}} \text{ turning point(s)} \]
#### (d) Use a graphing utility to graph the function and verify your answers.
### Graph Descriptions:
1. **Top Left Graph:**
- Displays the function \( h(t) \) with a vertex at \( t = 4 \), showing a parabolic shape opening upwards. The axis of symmetry appears at \( t = 4 \), and the graph crosses the y-axis near the point (0, 16).
2. **Top Right Graph:**
- Similar configuration: a parabola with upward direction. The focus seems to be around the point (4, 0), reinforcing symmetry around \( t = 4 \).
3. **Bottom Left Graph:**
- Displays a partial view of the parabola with its bottom visible, representing a vertex nearly centered at \( (4, 0) \).
4. **Bottom Right Graph:**
- A full parabola is drawn, confirming the function’s properties with a smoother curvature focused symmetrically around the line \( t = 4 \).
These graphs illustrate the characteristics of the quadratic function \( h(t) = t^2 - 8t + 16 \), helping to visualize solutions and analyze features such as turning points and symmetry.
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