A parabola intersects the xxx-axis at x=3x=3x, equals, 3 and x=9x=9x, equals, 9. What is the xxx-coordinate of the parabola's vertex?
Hint #11 / 3
Recall that the vertex is on the parabola's axis of symmetry.
How can this help us find the vertex's xxx-coordinate?
Hint #22 / 3
Since the vertex is on the axis of symmetry, it will be exactly between the two xxx-intercepts:
A parabola crosses the x-axis at 2 points. A vertical line intersect the x-axis halfway between those 2 points and intersects the parabola at its vertex.
So to find the vertex's xxx-coordinate, we can take the average of the two zeros:
\dfrac{9+3}{2}=6
2
9+3
​
=6