[tex]y=(3/5)x^2+30x+382[/tex]
The vertex form is
[tex]y=a(x-h)^2 + k[/tex]
To get vertex form , we apply completing the square method
For completing the square method we need x^2 alone
factor out 3/5 from first two terms
[tex]y= \frac{3}{5} x^2+30x+382[/tex]
When we factor out 3/5, we multiply by 5/3
[tex]y= \frac{3}{5}(x^2+50x)+ 382[/tex]
Now we take middle term divide by 2 and square it
50 divide by 2 = 25
25^2 = 625
Now we add and subtract 625
[tex]y= \frac{3}{5}(x^2+50x+625 -625)+ 382[/tex]
Take out -625 and multiply with 3/5 and add it with 382
[tex]y= \frac{3}{5}(x^2+50x+625) -625* \frac{3}{5}+ 382[/tex]
[tex]y= \frac{3}{5}(x^2+50x+625) -375+ 382[/tex]
[tex]y= \frac{3}{5}(x^2+50x+625) +7[/tex]
Now factor x^2 + 50x+625 and write it in square form
[tex]y= \frac{3}{5}(x+25)(x+25) +7[/tex]
[tex]y= \frac{3}{5}(x+25)^2 +7[/tex]
We got vertex form
Vertex is (h,k)
From our equation , h=-25 and k =7
So vertex is (-25,7)
To find y intercept we plug in 0 for x in the original equation
[tex]y= \frac{3}{5}(0)^2+30(0)+382[/tex]
y=382
So y intercept is (0,382)
