A quadratic function f is given. f(x) = x² + 8x + 15 (a) Express fin standard form. (b) Find the vertex and x- and y-intercepts of f. (If an answer does not exist, enter DNE.) (x, y) = vertex x-intercepts (x, y) = (x, y) = y-intercept (x, y) = (c) Sketch a graph of f. (smaller x-value) (larger x-value)
A quadratic function f is given. f(x) = x² + 8x + 15 (a) Express fin standard form. (b) Find the vertex and x- and y-intercepts of f. (If an answer does not exist, enter DNE.) (x, y) = vertex x-intercepts (x, y) = (x, y) = y-intercept (x, y) = (c) Sketch a graph of f. (smaller x-value) (larger x-value)
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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Question
Please see attached.
![**Quadratic Function Exploration**
A quadratic function \( f \) is given.
\[ f(x) = x^2 + 8x + 15 \]
**(a) Express \( f \) in standard form.**
\[ f(x) = \boxed{ } \]
**(b) Find the vertex and x- and y-intercepts of \( f \). (If an answer does not exist, enter DNE.)**
- **Vertex** \((x, y) = \left(\boxed{ }, \boxed{ }\right)\)
- **x-intercepts**
- \((x, y) = \left(\boxed{ }, \boxed{ }\right)\) (smaller x-value)
- \((x, y) = \left(\boxed{ }, \boxed{ }\right)\) (larger x-value)
- **y-intercept** \((x, y) = \left(\boxed{ }, \boxed{ }\right)\)
**(c) Sketch a graph of \( f \).**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36f9046e-a34d-43f2-ba4c-c4d16262d63e%2F12e9efff-8a8a-4236-bd34-cfba86c755f5%2Fakm4zqj_processed.png&w=3840&q=75)
Transcribed Image Text:**Quadratic Function Exploration**
A quadratic function \( f \) is given.
\[ f(x) = x^2 + 8x + 15 \]
**(a) Express \( f \) in standard form.**
\[ f(x) = \boxed{ } \]
**(b) Find the vertex and x- and y-intercepts of \( f \). (If an answer does not exist, enter DNE.)**
- **Vertex** \((x, y) = \left(\boxed{ }, \boxed{ }\right)\)
- **x-intercepts**
- \((x, y) = \left(\boxed{ }, \boxed{ }\right)\) (smaller x-value)
- \((x, y) = \left(\boxed{ }, \boxed{ }\right)\) (larger x-value)
- **y-intercept** \((x, y) = \left(\boxed{ }, \boxed{ }\right)\)
**(c) Sketch a graph of \( f \).**
Expert Solution
Step 1
Part
The standard form of a quadratic equation is .
We have .
This is already in standard form.
So, the standard form is .
Step by step
Solved in 3 steps with 2 images
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