Question

Could i have some super super quick help? :(( (part iv is not necessary)

might be getting the hang of it but i would still like some help

Answer 1

• y=-x²+16x-64

#1

• y=-x²+8x+8x-64
• y=-x(x+8)+8(x+8)
• y=(x+8)(-x+8)
• y=-(x-8)(x-8)

#2

Zeros are the x intercepts

Here they are

• 8,8

#3

• y=-x²+16x-64
• y=-[x²-16x+64]
• y=-(x-8)²+0

Vertex form of parabola:-y=a(x-h)²+k

• Vertex=(h,k)=(8,0)

#4

Attached

Answer 2

i)

Factor using completing square method

`\dashrightarrow \sf y = -x^2+16x-64`

`\dashrightarrow \sf y = -(x^2-16x+64)`

`\dashrightarrow \sf y = -(x^2-8x-8x+64)`

`\dashrightarrow \sf y = -(x(x-8)-8(x-8))`

`\dashrightarrow \sf y = -((x-8)(x-8))`

ii)

Find zeros of a function, f(x) = 0

`\dashrightarrow \sf -((x-8)(x-8))=0`

`\dashrightarrow \sf (x-8)=0, \ (x-8)=0`

`\dashrightarrow \sf x = 8`

iii)

In order to find vertex use the formulae : x = -b/2a

`\dashrightarrow \sf x = (-(16))/(2(-1))`

`\dashrightarrow \sf x = 8`

Then find y:

`\dashrightarrow \sf y = -(8)^2+16(8)-64`

`\dashrightarrow \sf y = 0`

coordinates: (8, 0)

iv) Sketched Below: