i)
Factor using completing square method
[tex]\dashrightarrow \sf y = -x^2+16x-64[/tex]
[tex]\dashrightarrow \sf y = -(x^2-16x+64)[/tex]
[tex]\dashrightarrow \sf y = -(x^2-8x-8x+64)[/tex]
[tex]\dashrightarrow \sf y = -(x(x-8)-8(x-8))[/tex]
[tex]\dashrightarrow \sf y = -((x-8)(x-8))[/tex]
ii)
Find zeros of a function, f(x) = 0
[tex]\dashrightarrow \sf -((x-8)(x-8))=0[/tex]
[tex]\dashrightarrow \sf (x-8)=0, \ (x-8)=0[/tex]
[tex]\dashrightarrow \sf x = 8[/tex]
iii)
In order to find vertex use the formulae : x = -b/2a
[tex]\dashrightarrow \sf x = \dfrac{-(16)}{2(-1)}[/tex]
[tex]\dashrightarrow \sf x = 8[/tex]
Then find y:
[tex]\dashrightarrow \sf y = -(8)^2+16(8)-64[/tex]
[tex]\dashrightarrow \sf y = 0[/tex]
coordinates: (8, 0)
iv) Sketched Below:
