Show that the function f(x) = x^2 + 2x + 2 is always positive for real values of x
By completing the square we find that f(x) = x2 + 2x + 2 = (x+1)2 + 1Since (x+1)2 is a number that has been squared, it must be greater than or equal to zero. Therefore, f(x) = (x+1)2 + 1 must be greater than zero because adding a positive number to a number that is greater than or equal to zero will always give a positive number.
BC
Related Maths GCSE answers
All answers ▸Multiply out and simplify (x+7)(x-3)
Simplify the following equation: x^(2) +3x+4^(2)-2
A plane travels at the speed of 213 miles per hour. Work out an estimate for the number of seconds it takes a plane to travel 1 mile.
P has coordinates (0, -1) and Q has coordinates (4, 1). a) Find the equation of line PQ. b) P and Q are two vertices of rectangle PQRS. Find the equation of line QR.