a. Express 7 + 5x - x 2 in the form a - (x + b) 2

Question:

a. Express 7 + 5x - x² in the form a - (x + b)², where a, and b are constants.

f(x) = 7 + 5x - x² for 0 ≤ x ≤ 7

b. Find the coordinates of the turning point of the function f(x), stating whether it is a maximum or minimum point.

c. Find the range of f.

d. State, giving a reason, whether or not f has an inverse.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Cambridge IGCSE And O Level Additional Mathematics Coursebook

ISBN: 9781108411660

2nd Edition

Authors: Sue Pemberton

See More Books

Question Posted: Aug 17, 2021 06:28 AM

See More Questions

a. Express 1 + 4x - x 2 in the form a - (x + b) 2 , where a and b are constants to be found. f(x) = 1 + 4x - x 2 for x 2 b. Find the coordinates of the turning point of the function f(x), stating...
Express the function in the form f o g o h. 51. H(x) = 1 - z 53. H(x) = sectT) 52. H(x) = X - 1
State whether the function is linear or quadratic. a. f (x) = 4 - 5x b. f (x) = 4 - 5x2 c. f (x) = 7x2 d. f (x) = 23x + 6
A credit card contains 16 digits. It also contains a month and year of expiration. Suppose there are one million users of a credit card with unique card numbers. A hacker randomly selects a 16 digit...
Discuss the role of marketing research in helping Intel devise the "Intel Inside" and "Leap ahead" campaigns.
The following covenants are extracted from a bond indenture. The indenture provides that failure to comply with its terms in any respect automatically advances the due date of the loan to the date of...
VLM Food Trading International, Inc. was a Canadian agricultural supplier. Starting in June 2012, VLM sold frozen potatoes to Illinois Trading Company, an Illinois produce distributor, through nine...
On January 4, 2014, Glennside Co. paid $235,000 for a computer system. In addition to the basic purchase price, the company paid a setup fee of $1,100, $6,200 sales tax, and $37,200 for a special...
The following trial balance was extracted from the books of accounts of KOWA partnership operated by Kori and Wangui partners for the period ended 31/12/2018 after preparing a trading account. KOWA...
Section C The programs at Denison consume the services of departments as follows: That is, oncology patients consume 80 percent of the services of the radiology department but only 50 percent of the...
Find the smallest value of m for which f has an inverse. f(x) = 4x 2 + 6x - 8 where x m
Find the value of k for which the curve y = 2x 2 - 3x + k i. Passes through the point (4, -7), ii. Meets the x-axis at one point only.
The Canadian Constitution gives the provinces control over property and civil rights, which includes the regulation of credit and registration of property as security for credit. Do the benefits to...
As a college student who relies on a seamless internet connection for both home and campus network activities, identify the optimal internet package offered by an Internet Service Provider (ISP) that...
3. What two different premiums are applied when calculating Worker's Compensation rates.
What did USA Hockey learn when they attempted to recruit scabs to replace team members? What is your reaction to the willingness of other players and unions to say "No" to USAH and support...
Calculate the Value of Assets 0% Debt/ 25% Debt/ 50% Debt/ 100% Equity 75% Equity 50% Equity Book Value of Debt Book Value of Equity $2,500 $5,000 $10,000 $7,500 $5,000 Market Value of Debt $2,500...
Icarus Airlines is proposing to go public, and you have been given the task of estimating the value of its equity. Management plans to maintain debt at 40% of the company's present value, and you...
When prices of used cars dropped about 10 percent in October 2001, their sales increased by 4.5 percent. Does this mean that the demand elasticity for used cars is 0.45?
The following selected accounts and normal balances existed at year-end. Notice that expenses exceed revenue in this period. Make the four journal entries required to close the books: Accounts...
The curve and the line x 2y + 6 = 0 intersect at the points A and B. a. Find the coordinates of these two points. b. Find the perpendicular bisector of the line AB. y=x+2. 4 X
A is the point (0, 8) and B is the point (8, 6). Find the point C on the y-axis such that angle ABC is 90.
Two circles have the following properties: The x-axis is a common tangent to the circles The point (8, 2) lies on both circles The centre of each circle lies on the line x + 2y = 22. a. Find the...
External auditors play an important role in ensuring compliance with corporate governance principles through the protection of shareholders' interests. Critically evaluate the role of the external...
1. When undergraduate students are trying to determine which university to attend for a master's program, they know that it is very important for their future and they know that there are a wide...
What is Blackstone's theory of environmental rights?

a. Express 7 + 5x - x 2 in the form a - (x + b) 2

Question:

Step by Step Answer:

A by expanding the given form a xb 2 we find that a xb 2 a x 2 2bxb 2 a b 2 2bx x 2 comparing it to ...View the full answer

Cambridge IGCSE And O Level Additional Mathematics Coursebook

Students also viewed these Business questions