The parabola given by the equation y = x² + 7x + 18 can be analyzed based on its standard form. To determine the direction in which it opens, we first need to identify the leading coefficient of the quadratic term, which is the coefficient of x².
In this equation, the coefficient of x² is 1 (since the equation can be rewritten as y = 1x² + 7x + 18). The sign of the leading coefficient plays a crucial role in determining the direction:
- If the leading coefficient is positive (greater than 0), the parabola opens upward.
- If the leading coefficient is negative (less than 0), the parabola opens downward.
Since the coefficient here is 1, which is positive, we can conclude that the parabola opens upward.
To further visualize this, you can complete the square or find the vertex of the parabola, but simply looking at the leading coefficient is sufficient for determining the direction of opening.
In summary, the parabola defined by the equation y = x² + 7x + 18 opens upward.