Question

how does the sign of the coefficient ( a ) in ( y = ax^2 + bx + c ) determine the direction the parabola opens?

a. positive ( a ) opens left, negative ( a ) opens right.

b. positive ( a ) opens right, negative ( a ) opens left.

c. positive ( a ) opens downwards, negative ( a ) opens upwards.

d. positive ( a ) opens upwards, negative ( a ) opens downwards.

Explanation:

The given equation $y = ax^2 + bx + c$ is a vertical parabola. For vertical parabolas, the sign of the leading coefficient $a$ determines the opening direction: a positive $a$ makes the parabola open upwards, while a negative $a$ makes it open downwards. Options a and b describe horizontal parabolas (which have the form $x = ay^2 + by + c$), so they are incorrect. Option c reverses the correct relationship for vertical parabolas.

Answer:

d. Positive a opens upwards, negative a opens downwards.