The vertex of the parabola is (6, -9). The vertex form of the given parabola is y = (x - 6)^2 - 9.
The general form of the parabola is y=ax^2+bx+c
The vertex of the parabola is (h, k) and the vertex form of the parabola is [tex]y = (x - h)^2 + k[/tex]
Where x- coordinate of the vertex = h = -b/2a.
The given x-intercepts are x1 = 3 and x2 = 9.
So, Writing the equation as
(x - x1)( x - x2) =0
(x - 3)(x - 9) = 0
x²-12x + 27 = 0
Thus, on comparing,
a = 1, b=12 c= 27
So, calculating the h = -b/2a
⇒ h = -(-12)/2×1
∴ h = 6
On substituting h in the vertex form of the parabola,
y = (x - h)² + k
⇒ y = (x - 6)² + k
Since the parabola is passing through (3, 0) (parabola intersects at x=3)
⇒ 0 = (3 - 6)² + k
∴ k = -9
So, the vertex of the given parabola is (6, -9).
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