Question

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

Answer 1

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

$\dashrightarrow \sf x = \dfrac{-(16)}{2(-1)}$

$\dashrightarrow \sf x = 8$

Then find y:

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

$\dashrightarrow \sf y = 0$

coordinates: (8, 0)

iv) Sketched Below:

Answer 2

• 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