To find the x-coordinate of the vertex of the parabola given by the equation y = 3x² + 9x, we can use the vertex formula, which is derived from the standard form of a quadratic equation y = ax² + bx + c.
In this equation, a is the coefficient of x², b is the coefficient of x, and c is the constant term. Here, we see that:
- a = 3
- b = 9
- c = 0
The x-coordinate of the vertex can be calculated using the formula:
x = -b / (2a)
Plugging in the values for b and a:
x = -9 / (2 * 3) = -9 / 6 = -3/2
Therefore, the x-coordinate of the vertex of the parabola represented by the equation y = 3x² + 9x is -1.5 or -3/2.