For the function f(x) = 2x^2-31x-51, where is the function increasing and positive? ( for all x values greater than what number )

ANSWER


EXPLANATION

The given function is


Let us split the middle term to get,



We factor to obtain,





Let us find the zeros of f(x),



Either




We need to find the x-value of the vertex, which is the midpoint of the x-intercepts.

This gives us,


Hence the axis of symmetry of the parabola has equation,



Since the given function has minimum turning point, it will decrease and then increase.

The function will be increasing for


The function will be increasing and positive for