Answer:
(8,-3)
Step-by-step explanation:
The given parabola is
[tex]y = - 3 {x}^{2} + 48x - 195[/tex]
We factor -3 from the first two terms to get:
[tex]y = - 3( {x}^{2} - 16x) - 195[/tex]
Add and subtract the square of half the coefficient of x
[tex]y = - 3( {x}^{2} - 16x + 64) + 3 \times 64- 195[/tex]
[tex]y = - 3 {(x - 8)}^{2} + 192 - 195[/tex]
We simplify to get:
[tex]y = - 3 {(x - 8)}^{2} - 3[/tex]
We compare this to y=a(x-h)²+k,
The vertex is (h,k)=(8,-3)
