Question

which of the following describes the direction of opening for $y = -2x^2 + 3x - 1$?
options: opens upward, opens left, opens right, opens downward

Explanation:

Step1: Recall parabola opening rule

For a quadratic function \( y = ax^2 + bx + c \), the direction of opening is determined by the coefficient \( a \). If \( a>0 \), the parabola opens upward; if \( a<0 \), it opens downward.

Step2: Identify \( a \) in the given function

In the function \( y = -2x^2 + 3x - 1 \), the coefficient of \( x^2 \) (i.e., \( a \)) is \( -2 \).

Step3: Determine the direction

Since \( a = -2 < 0 \), the parabola opens downward.

Answer:

Opens downward