Determine whether the a-value is positive or negative. Provide an appropriate reason. (1 point) Responses
The a-value is negative because the graph is of a parabola that opens down.
The a-value is positive because the graph is of a parabola that opens up.
The a-value is negative because the x-intercepts are negative.
The a-value is negative because the y-intercept is negative.
The correct response is: The a-value is positive because the graph is of a parabola that opens up.
The a-value in the standard form equation of a parabola, y = ax^2 + bx + c, determines the direction and shape of the graph. If the a-value is positive, the graph opens upward and forms a U shape. If the a-value is negative, the graph opens downward and forms an upside-down U shape. Therefore, from the given information that the graph is of a parabola that opens up, we can conclude that the a-value must be positive.