Here we are given the x intercepts at x=3 and x=9
So let us try to make quadratic equation for this using given information.
We have factors in the form (x-a)(x-b)
where a and b are x intercepts given to us.
So rewriting in factored form:
![y=(x-3)(x-9)](https://tex.z-dn.net/?f=y%3D%28x-3%29%28x-9%29)
Now let us simplify it:
![y=x^{2}-12x+27](https://tex.z-dn.net/?f=y%3Dx%5E%7B2%7D-12x%2B27)
Let us find the vertex now,
For a quadratic equation of the form:
![y=ax^{2}+bx+c](https://tex.z-dn.net/?f=y%3Dax%5E%7B2%7D%2Bbx%2Bc)
For x coordinate , we have the formula,
![x=\frac{-b}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%7D%7B2a%7D)
So using this formula for our equation,
![x=\frac{-(-12)}{2(1)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-%28-12%29%7D%7B2%281%29%7D)
So x = 6
Answer: The x-coordinate of the parabola's vertex is 6.