A function is defined by $\displaystyle x^2+2x+c$ for $\displaystyle x$ is a real number. Find the value of the constant $\displaystyle c$ for which the range of f is given by $\displaystyle f(x)$≥$\displaystyle 3$
From "the range of f is given by y≥3" can I say that the equation $\displaystyle x^2+2x+c$ is always positive and hence $\displaystyle b^2-4ac<0$ and solve for the range of c?
I dont know if this is the right way to solve, but i really dont understand how to solve the question even after all of your help...
i am afraid i might need more explanation, i am sorry for wasting your time
You should know that the range of a positive parabola is all the values of y equal to or greater than the y-coordinate of the turning point.
In your question you have a positive parabola and it has been pointed out to you that the y-coordinate of the turning point is c - 1. Therefore .....
That's good.
But since this question has been posted in the PRE-calculus subforum, the expectation of members is that it will be solved without using calculus. That's why post #3 completes the square. Do you know how to complete the square and do you know how to read the coordinates of the turning point from y = a(x - h)^2 + k?