In the quadratic function y = ax^2 + bx + c, the parabola opens upward if a > 0 and downward if a < 0.

• A. True
• B. False
• C. It depends on b
• D. It depends on c

Answer: (A)

The direction a quadratic opens is determined by the sign of the coefficient in front of x^2. If that coefficient is positive, the x^2 term makes y grow without bound as x moves away from the vertex, so the parabola opens upward. If that coefficient is negative, y decreases without bound as |x| increases, and the parabola opens downward. The other coefficients, b and c, shift the graph or change its width but don’t change the direction of opening. For example, y = x^2 opens upward, while y = -x^2 opens downward; a positive a like in y = 2x^2 + 3x + 1 keeps the opening upward, though the vertex and width differ. So the statement is true.