a Express 3x 2 12x 1 in the form a(x b) 2 c, where a, b and c are constants b Write down the coordinates of the vertex of the curve y 3x 2 12x 1 c Find the set of values of k for which 3x 2 12x 1 kx 4 has no real solutions ...

2 2 a Completing the square to express 3x2 12x 1 in the form ax b2 c 3x2 12x 1 3x2 4x 1 3x2 ...

a. Express 3x 2 + 12x 1 in the form a(x + b) 2 + c,

Question:

a. Express 3x² + 12x − 1 in the form a(x + b)² + c, where a, b and c are constants.

b. Write down the coordinates of the vertex of the curve y = 3x² + 12x − 1.

c. Find the set of values of k for which 3x² + 12x − 1 = kx − 4 has no real solutions.

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

Step by Step Answer:

Related Book For book-img-for-question

Cambridge International AS And A Level Mathematics Pure Mathematics 1 Coursebook

ISBN: 9781108407144

1st Edition

Authors: Sue Pemberton, Julian Gilbey

See More Books

Question Posted: Mar 09, 2023 03:37 AM

See More Questions

Find the set of values of k for which the curve y - (k + 1)x 2 - 3x + (k + 1) lies below the x-axis.
Find the set of values of k for which the line y = 2x - 5 cuts the curve y = x 2 + kx + 11 in two distinct points.
Find the set of values of k for which the line y = 3x + 1 cuts the curve y = x 2 + kx + 2 in two distinct points.
Use the graphs of f and g to solve Exercises 8390. Find (fg)(2). y = g(x) HH y .y = f(x) # X
Suppose that the random variables X and Y represent the amount of return on two different investments. Further suppose that the mean of X equals the mean of Y but that the standard deviation of X is...
Presented here is selected information (in millions) from the 2010 financial statements of Rogers Communications Inc. and Shaw Communications Inc.: Instructions (a) Calculate the receivables turnover...
The optimum speeds (in kilometers per hour) for 30 hatchbacks Approximate the mean of the frequency distribution. Car Speeds (in kilometers per hour) Frequency 20-24 15 25-29 8. 30-34 4 35-39 3
Wedona Energy Consultants prepares adjusting entries monthly. Based on an analysis of the unadjusted trial balance at January 31, 2014, the following information was available for the preparation of...
Suppose a company is choosing between bank loans and bonds. A bank is offering an interest rate of 4.5% to lend the money to the firm and requires the company to post collateral and comply with...
There are three coins in a barrel. These coins, when flipped. will conic up heads with respective probabilities 0.3. 0.5.0.7. A coin is randomly selected from among these three and is then flipped...
The equation of a circle is x 2 + y 2 8x + 4y + 4 = 0. a. Find the radius of the circle and the coordinates of its centre. b. Find the x-coordinates of the points where the circle crosses the...
A curve has equation y = 12x x 2 . a. Express 12x x 2 in the form a (x + b) 2 , where a and b are constants to be determined. b. State the maximum value of 12x x 2 . The function g is defined as...
At the time of her death on September 4, 2012, Alicia held the following assets. __________________________________________ Fair Market Value Bonds of Emerald Tool Corporation...
The following are summary financial statements for Kuala Lumpur DIY Plc. Non-current assets Current assets Total assets 20X4 $000 20X9 $000 115 410 650 1,000 765 1,410 Capital and reserves 210 270...
Chris Smith - Owner and Senior Accountant B.Ec. (Accounting major), M.Tax (UNSW), FIPA Director Chris is a registered tax agent and an accountant who has been in public practice as an accountant...
5) A particle of mass 0.50 kg moves along the x-axis with a potential energy whose dependence on x is shown below. What is the force on the particle from x=6.0 to x=10m A) 6N C) 4N B) -6N D) 8N...
Provide The Payoff Function (On The Table) For Each Range Strike Prices In Which The Stock Price Could Land At Expiration. There Are Three Ranges In Which The Stock Price Could At Land At Expiration,...
SOLVE THE FOLLOWING PROBLEMS AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR ANSWER FOR BETTER UNDERSTANDING. 1. Find the interest and amount on PhP 10,500 at 8% simple interest for 10 months. 2. Find...
Lucy, from Problem 4, spends all her income on lemonade, which costs $1 per pint. She earns $300 per month, but is robbed with 25 percent probability, in which case she is left with only $100. She...
In the operation of an automated production line with storage buffers, what does it mean if a buffer is nearly always empty or nearly always full?
A university investigated how much space on its computers hard drives is used for data storage. The results are shown below. It is given that 40 hard drives use less than 20GB for data storage. a....
Eighty people downloaded a particular application and recorded the time taken for the download to complete. The times are given in the following table. a. Find the number of downloads that completed...
A railway line monitored 15% of its August train journeys to find their departure delay times. The results are shown below. It is given that 24 of these journeys were delayed by less than 2 minutes....
Esquire Company needs to acquire a molding machine to be used in its manufacturing process. Two types of machines that would be appropriate are presently on the market. The company has determined the...
On December 31, 2024, when its Allowance for Doubtful Accounts had a debit balance of $1,371, Sandhill Co. estimates that 8% of its accounts receivable balance of $77,800 will become uncollectible...
Using basic HTML5 and CSS3, create a series of webpages with a simple structure incorporating a unified theme. The HTML must contain at least the following items: The first page will be called...

a. Express 3x 2 + 12x 1 in the form a(x + b) 2 + c,

Question:

Step by Step Answer:

2 2 a Completing the square to express 3x2 12x 1 in the form ax b2 c 3x2 12x 1 3x2 4x 1 3x2 ...View the full answer

Cambridge International AS And A Level Mathematics Pure Mathematics 1 Coursebook

Students also viewed these Mathematics questions