Homework Help is Here – Start Your Trial Now!
Math
Algebra
7 f(x) = 4x² - 8x + 2 for x € R, 0 < x < k a Express f(x) in the form a (x +6²) + c. b State the value of k for which the graph of y = с For your value of k from part b, find the range of f. f(x) has a line of symmetry.

7 f(x) = 4x² - 8x + 2 for x € R, 0 < x < k a Express f(x) in the form a (x +6²) + c. b State the value of k for which the graph of y = с For your value of k from part b, find the range of f. f(x) has a line of symmetry.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
See similar textbooks
icon
Related questions
Question
100%

Please help me answer the entirety of number 7

Sure! Here is the transcription of the text from the image: --- 3. Express each function in the form \( a(x+b)^2+c \), where \( a, b, \) and \( c \) are constants and hence state the range of each function. a. \( f(x) = x^2 + 4x - 1 \) for \( x \in \mathbb{R} \) b. \( f(x) = 2x^2 - 4x + 3 \) for \( x \in \mathbb{R} \) 4. Express each function in the form \( a - b(x+c)^2 \), where \( a, b, \) and \( c \) are constants and hence state the range of each function. a. \( f(x) = 3 - 2x - x^2 \) for \( x \in \mathbb{R} \) b. \( f(x) = 1 - 6x - x^2 \) for \( x \in \mathbb{R} \) 5. The function \( g : x \mapsto 6 + 3ax - 3x^2 \), where \( a \) is a constant is defined for \( x \in \mathbb{R} \). Find the range of \( g \) in terms of \( a \). 6. \( f(x) = x^2 - 4 \) for \( x \in \mathbb{R}, -a \leq x \leq a \) If the range of the function \( f \) is \(-4 \leq f(x) \leq 5\), find the value of \( a \). 7. \( f(x) = 4x^2 - 8x + 2 \) for \( x \in \mathbb{R}, 0 \leq x \leq k \) a. Express \( f(x) \) in the form \( a(x+b)^2+c \). b. State the value of \( k \) for which the graph of \( y = f(x) \) has a line of symmetry. c. For your value of \( k \) from part b, find the range of \( f \). --- **TIP** If we draw all possible vertical lines on the
Transcribed Image Text:Sure! Here is the transcription of the text from the image: --- 3. Express each function in the form \( a(x+b)^2+c \), where \( a, b, \) and \( c \) are constants and hence state the range of each function. a. \( f(x) = x^2 + 4x - 1 \) for \( x \in \mathbb{R} \) b. \( f(x) = 2x^2 - 4x + 3 \) for \( x \in \mathbb{R} \) 4. Express each function in the form \( a - b(x+c)^2 \), where \( a, b, \) and \( c \) are constants and hence state the range of each function. a. \( f(x) = 3 - 2x - x^2 \) for \( x \in \mathbb{R} \) b. \( f(x) = 1 - 6x - x^2 \) for \( x \in \mathbb{R} \) 5. The function \( g : x \mapsto 6 + 3ax - 3x^2 \), where \( a \) is a constant is defined for \( x \in \mathbb{R} \). Find the range of \( g \) in terms of \( a \). 6. \( f(x) = x^2 - 4 \) for \( x \in \mathbb{R}, -a \leq x \leq a \) If the range of the function \( f \) is \(-4 \leq f(x) \leq 5\), find the value of \( a \). 7. \( f(x) = 4x^2 - 8x + 2 \) for \( x \in \mathbb{R}, 0 \leq x \leq k \) a. Express \( f(x) \) in the form \( a(x+b)^2+c \). b. State the value of \( k \) for which the graph of \( y = f(x) \) has a line of symmetry. c. For your value of \( k \) from part b, find the range of \( f \). --- **TIP** If we draw all possible vertical lines on the
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS