Question

Need help with this math question

Answer 1

Answer: 6, 8

Explanation:

Answer 2

The vertex is:
`(6, 8)`

Explanation:

First solve the equation for the variable y

`x^2-4y-12x+68=0`

Add 4y on both sides of the equation

`4y=x^2-4y+4y-12x+68`

`4y=x^2-12x+68`

Notice that now the equation has the general form of a parabola

`ax^2 +bx +c`

In this case

`a=1\\b=-12\\c=68`

Add
`((b)/(2)) ^ 2` and subtract
`((b)/(2)) ^ 2` on the right side of the equation

`((b)/(2)) ^ 2=((-12)/(2)) ^ 2\\\\((b)/(2)) ^ 2=(-6) ^ 2\\\\((b)/(2)) ^ 2=36`

`4y=(x^2-12x+36)-36+68`

Factor the expression that is inside the parentheses

`4y=(x-6)^2+32`

Divide both sides of the equality between 4

`(4)/(4)y=(1)/(4)(x-6)^2+(32)/(4)`

`y=(1)/(4)(x-6)^2+8`

For an equation of the form

`y=a(x-h)^2 +k`

the vertex is: (h, k)

In this case

`h=6\\k =8`

the vertex is:
`(6, 8)`