Question: The function f is defined as f(x) = x 2 2x + 2, x. a. Write f(x) in the form (x + p) 2

The function f is defined as f(x) = x2 − 2x + 2, x ∈ ℝ.

a. Write f(x) in the form (x + p)2 + q, where p and q are constants to be found.

b. Hence, or otherwise, explain why f(x) > 0 for all values of x, and find the minimum value of f(x).

Step by Step Solution

★★★★★

3.40 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a To write fx in the form x p2 q we need to complete the square Let... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Edexcel AS And A Level Mathematics Questions!

Q:

Case 3.1. Chinese are moving to Africa to make shoes Shoemakers are the wildebeests of global trade, migrating to wherever the grass is greenest-or in their case, labor costs are lowest. Huajian...

Q:

A function f is defined by f(x) = 1 + 2x + x2 + 2x3 + x4 + ... that is, its coefficients are c2n = 1 and c2n+1 = 2 for all n ( 0. Find the interval of convergence of the series and find an explicit...

Q:

A model rocket is launched upward from an altitude of 190 feet. Its height in feet, h, after t seconds, can be modeled by the equation h (t) = -16 t2 + 176 t + 190, t > 0. During what time interval...

Q:

7 The function f is defined as f (x) = 2.x- - 4 Find f (x -6). Write your answer without parentheses, and simplify it as much as possible. f (x - 6) = 0 X 5The functions f and g are defined as...

Q:

The one-to-one function f is defined below. f ( x ) = 5x - 1 2x+ 3 Find f (x), where f is the inverse of f. Also state the domain and range of f * in interval notation. 1' ( x ) = (0,0) [0,0] OVO...

Q:

The function g is defined as g (x) = 3x 2 - 2x Find g (x + 5). Write your answer without parentheses, and simplify it as much as possible. Full-screen g (x +5) = 1 X 5

Q:

Please help with math problem as fast as you can. Thank you 10 [Maximum mark: 5] The function f is defined as f (x) = 3x + 2. x+1 ,XER, x#-1. Sketch the graph of y =f (x), clearly indicating and...

Q:

7 The function h is defined as h (x) = - 3x- - 2 Find h (x - 5). Write your answer without parentheses, and simplify it as much as possible. 10 h (x - 5) = 1 X

Q:

The function h is defined as h (x) = 3x -2. Find h (x + 5). Write your answer without parentheses, and simplify it as much as possible. h (x + 5 ) = 1 X

Q:

1) State the initial value theorem. Verify the theorem for the functions (a) 3 4 sin t (b) (t 4)2 and state their initial values. [(a) 3 (b) 16] 2. Verify the initial value theorem for the voltage...

Q:

How does the relationship between price movements and employment at the country level differ from the relationship between price movements and employment at the firm level?

Q:

To what future value will the Question 4 amount grow over the subsequent 19 years?