Question

For a quadratic function ƒ(x)=ax2+bx+c, ƒ(−1)<1, ƒ(1)>−1, and ƒ(3)<−4. What could be the sign of a?

Answer 1

"a" must be negative

Explanation:

The slope between points (-1, 1) and (1, -1) is a minimum of (-1-1)/(1-(-1)) = -1.

The slope between points (1, -1 and (3, -4) is a maximum of (-4-(-1))/(3-1) = -3/2.

Thus, as x increases, the slope is decreasing. In order for that to be the case, the value of a must satisfy a < 0.