A quadratic function f is given. f(x) = x² + 4x - 1 (a) Express fin standard form. f(x) = (b) Sketch a graph of f.
A quadratic function f is given. f(x) = x² + 4x - 1 (a) Express fin standard form. f(x) = (b) Sketch a graph of f.
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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![### Quadratic Function Exercise
A quadratic function \( f \) is given:
\[ f(x) = x^2 + 4x - 1 \]
#### (a) Express \( f \) in standard form.
\[ f(x) = \boxed{\phantom{x}} \]
#### (b) Sketch a graph of \( f \).
**Instructions:**
1. **Standard Form Conversion:**
- The given quadratic function is in the form \( ax^2 + bx + c \).
- Convert it into the standard form \( a(x - h)^2 + k \) by completing the square.
2. **Graph Sketching:**
- Identify the vertex, axis of symmetry, and direction of the parabola.
- Use this information to sketch the graph accurately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36f9046e-a34d-43f2-ba4c-c4d16262d63e%2Ff46add8d-84a2-4443-90ab-f4fe063a2f1a%2Fpq3pr4d_processed.png&w=3840&q=75)
Transcribed Image Text:### Quadratic Function Exercise
A quadratic function \( f \) is given:
\[ f(x) = x^2 + 4x - 1 \]
#### (a) Express \( f \) in standard form.
\[ f(x) = \boxed{\phantom{x}} \]
#### (b) Sketch a graph of \( f \).
**Instructions:**
1. **Standard Form Conversion:**
- The given quadratic function is in the form \( ax^2 + bx + c \).
- Convert it into the standard form \( a(x - h)^2 + k \) by completing the square.
2. **Graph Sketching:**
- Identify the vertex, axis of symmetry, and direction of the parabola.
- Use this information to sketch the graph accurately.
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