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 ▸Solve the following simultaneous equations: 4x+y=10 and 2x-3y=19
Prove that 12 cos(30°) - 2 tan(60°) can be written as √k where k is an integer, state the value of k.
Simplify (x^5 * x^8)/(x^4 * x^4).
A curve (a) has equation, y = x^2 + 3x + 1. A line (b) has equation, y = 2x + 3. Show that the line and the curve intersect at 2 distinct points and find the points of intersection. Do not use a graphical method.