Aparabola intersects the x-axis at x=3 and x=9 what is the x-coordinate of the parabola's vertex?

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:

Now let us simplify it:

Let us find the vertex now,

For a quadratic equation of the form:

For x coordinate , we have the formula,

So using this formula for our equation,

So x = 6

The x-coordinate of the parabola's vertex is 6.

The -coordinate of the parabola's vertex is 6

The intercepts at and

The factors are in the form  

where and are intercepts given to us.

So rewriting in factored form:

Now simplify it:

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find the vertex now,

A quadratic equation form is:

----------

So compare equation and ,we get

For coordinate , we have the formula,

So

The x-coordinate of the parabola's vertex is .

Learn more about Parabola here;

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y - y1 = m(x- x1)

y - (-5) = 2/3(x -0)

y + 5 = 2/3x

y = 2/3x - 5

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