Fine the intervals on which the function f(x)= ax^2 +bx+c (where “a” doesn’t =0) is increasing and decreasing.

Question

Describe the reasoning behind your answer.

Answer 1

The axis of symmetry is at x = -b / 2a

If a > 0, then f(x) is decreasing for x < -b / 2a and increasing afterward

If a < 0, then f(x) is increasing for x , -b / 2a and decreasing afterward

Answer 2

Andrea

There are two cases. a>0 and a<0.

If a>0 this is a quadratic, concave down, with the vertex (minimum) at the bottom.

So you need to find the x coordinate of that vertex. f'(x) = 0 will give you that.

Obviously if X is the x coordinate of the vertex, the function will be decreasing on (-∞,X) and increasing on (X,+∞).

The other case, a<0, you can try and figure out.

Mike