Question

Using the equation y=ax^2+bx+c to represent a parabola on a graph, which statement is true?

1) If b is negative, the parabola opens downward
2) If a is negative, the parabola opens upward
3) If a is positive, the parabola open upward
4) If c is negative, the parabola opens downward

Answer 1

Tha answer is 3) if a is positive, the parabola opens upward. You can see that when you imagine what happens when x is large. In that case bx + c is small compared to ax^2, and the value of the function is dominated by the terms ax^2. x^2 is positive always, so the sign of ax^2 is given by a. Then if a is positive the extreme values of the function (x positively large and x negatively large) are positive, which is the case when the parabola opens upward.