Concave up?.....

Question

Consider the parabolic function f(x) = ax² + bx + c , where a ≠ 0, b and c are constants. For what values of a, b and c is f.

Answer 1

Simply put, "Concave up" or "Concave down" just refers to which direction the function appears to 'bend' when graphed. A concave up function will curve upwards, so this question is really asking which values (a, b, or c) control whether this function is concave up? You can play with the constants on this graph using a calculator or [desmos dot com/calculator] to see if you can figure out what makes this function curve up or down.

Once you figure out how a, b, and c change the shape of the graph, the question asks you what values will give you a concave up graph.

Alternatively, as this has a calculus tag on it, you're looking for values of a, b, and c where the second derivative [f''(x)] of your function is positive. If you take the second derivative of f(x), leaving all the constants in place for the moment, when is it positive?