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:
[tex]y=(x-3)(x-9)[/tex]
Now let us simplify it:
[tex]y=x^{2}-12x+27[/tex]
Let us find the vertex now,
For a quadratic equation of the form:
[tex]y=ax^{2}+bx+c[/tex]
For x coordinate , we have the formula,
[tex]x=\frac{-b}{2a}[/tex]
So using this formula for our equation,
[tex]x=\frac{-(-12)}{2(1)}[/tex]
So x = 6
Answer: The x-coordinate of the parabola's vertex is 6.
The -coordinate of the parabola's vertex is 6
The [tex]x[/tex] intercepts at [tex]x=3[/tex] and [tex]x=9[/tex]
The factors are in the form [tex](x-a)(x-b)[/tex]
where and are intercepts given to us.
So rewriting in factored form:
[tex]y=(x-3)(x-9)[/tex]
Now simplify it:
[tex]y=x^{2}-12x+27[/tex]-------[tex]1[/tex]
find the vertex now,
A quadratic equation form is:
[tex]y=ax^{2}+bx+c[/tex]----------[tex]2[/tex]
So compare equation and ,we get
[tex]a=1 , b=-12 \;and\; c=27[/tex]
For coordinate , we have the formula,
[tex]x=\dfrac{-b}{2a}[/tex]
[tex]x=\dfrac{-2(-12)}{2(1)}[/tex]
So [tex]x=6[/tex]
The x-coordinate of the parabola's vertex is [tex]6[/tex] .
Learn more about Parabola here;
https://brainly.com/question/21685473?referrer=searchResults
