A parabola is graphed on a coordinate plane. The x-axis ranges from negative 10 to 3 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Determine whether the a-value is positive or negative. Provide an appropriate reason.
(1 point)
Responses
The a-value is negative because the x-intercepts are negative.
The a -value is negative because the x -intercepts are negative.
The a-value is negative because the y-intercept is negative.
The a -value is negative because the y -intercept is negative.
The a-value is negative because the graph is of a parabola that opens down.
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.
1 answer
The correct response is:
The a-value is negative because the graph is of a parabola that opens down.
This is because a parabola that opens downward has a negative a-value in its quadratic equation \(y = ax^2 + bx + c\). Conversely, a parabola that opens upward has a positive a-value. The orientation of the parabola is determined by the sign of the a-value.
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