Question

Which equation represents a graph with a vertex at (1, –6)?

A.y = 3x2 + 6x – 3
B.y = 3x2 – 6x – 3
C.y = 3x2 – 8x – 1
D.y = 3x2 – 3x – 6

Answer 1

Answer: B)
`y = 3x^2 - 6x - 3`

To find vertex (h,k) we use formula

`h=(-b)/(2a)`

To find out k we plug in 'h' value in the given equation

Lets find vertex for each equation

A)
`y = 3x^2 + 6x - 3`

`h=(-b)/(2a)=(-6)/(2*3)=-1`

Now plug in -1 for x,
`y = 3(-1)^2 + 6(-1) - 3=-6`

So vertex is (-1,-6)

B)
`y = 3x^2 - 6x - 3`

`h=(-b)/(2a)=(-(-6))/(2*3)=1`

Now plug in -1 for x,
`y = 3(1)^2 - 6(1) - 3=-6`

So vertex is (1,-6)

C.y =
`3x^2 - 8x - 1`

`h=(-b)/(2a)=(-(-8))/(2*3)=(4)/(3)`

Now plug in
`(4)/(3)` for x,
`y = 3((4)/(3))^2 - 8((4)/(3)) - 1= (-19)/(3)`

D.
`y = 3x^2 - 3x - 6`

`h=(-b)/(2a)=(-(-3))/(2*3)= (1)/(2)`

Now plug in 1/2 for x,
`y = 3((1)/(2))^2 - 3 ((1)/(2))- 6=(-27)/(4)`

So, option B has vertex (1,-6)

Answer 2

For the answer to the question above asking Which equation represents a graph with a vertex at (1, –6)?
The answer is the second one among the given choices which is B.y = 3x2 – 6x – 3
For the explanation,
write y+6=3(x^2-1)^2=>
y+6=3x^2-6x+3=>
y=3x^2-6x-3