a parabola intersects the x - axis at x = 3 and x = 9.\nwhat is the x - coordinate of the parabolas vertex?

Explanation:

Step1: Recall the property of parabola's axis of symmetry

The axis of symmetry of a parabola passes through the mid - point of the roots (where it intersects the (x) - axis). If the roots are (x_1) and (x_2), the formula for the (x) - coordinate of the axis of symmetry (and the vertex, since the vertex lies on the axis of symmetry) is (x=\frac{x_1 + x_2}{2}).

Step2: Substitute the given roots into the formula

Here, (x_1 = 3) and (x_2=9). Then (x=\frac{3 + 9}{2}). Calculate (\frac{3+9}{2}=\frac{12}{2}=6).

Answer:

6