Question

Need help with this math question

Answer 1

(-7, 4)

Explanation:

We are given the following equation for which we have to complete the square in order to find the vertex of this parabola:

`y ^ 2 - 4 x - 8 y - 1 2 = 0`

`y^2-((8)/(2) )^2-4x-12=((8)/(2) )^2\\`

`y ^ 2 - 1 6 - 4 x - 1 2 = 1 6`

`( y - 4 ) ^ 2 - 4 x - 1 2-16=0`

`(y-4)^2=4x+28`

`(y-4)^2=4(x+7)`

`x+7=0, y-4=0`

x = -7, y = 4

Therefore, the vertex of this parabola is (-7, 4).

Answer 2

The vertex of this parabola is (-7,4)

EXPLANATION

The given parabola has equation:

`{y}^(2) - 4x - 8y - 12 = 0`

`{y}^(2) - 8y = 4x +12`

Complete the square for the quadratic equation in y.

`{y}^(2) - 8y + {( - 4)}^(2) = 4x + 12 + {( - 4)}^(2)`

`{y}^(2) - 8y + {( - 4)}^(2) = 4x + 12 + 16`

`{( y- 4)}^(2) = 4x + 28`

`{( y- 4)}^(2) = 4(x +7)`

The vertex of this parabola is (-7,4)