Greetings!
As you already have the vertex, the equation for this is:
[tex]y = A(x - b)^{2} + k[/tex]
Where (b, k) is the vertex.
So by plugging all this in using the vertex coordinates you get:
[tex]y = 3(x - 3)^{2} - 2[/tex]
To find the x intercepts, you set the y value to 0, so:
[tex]0 = 3(x - 3)^{2} - 2[/tex]
Now you can move the negative two over, making it a positive two:
[tex]2= 3(x - 3)^{2}[/tex]
Now, if you divide everything by three you get:
[tex]\frac{2}{3} = (x - 3)^{2}[/tex]
Then you can simple square root both sides to get x - 3 by itself:
[tex]\sqrt{\frac{2}{3}} = x-3[/tex]
Then finally move the negative three over to the other side so that x is by itself:
3 ± [tex]\sqrt{\frac{2}{3}} = x[/tex]
Which means that the two x intercepts are:
([tex]3 + \sqrt{\frac{2}{3}}[/tex],0) and ([tex]3 - \sqrt{\frac{2}{3}}[/tex],0)
Hope this helps!
