Respuesta :

kudzordzifrancis

ANSWER

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

EXPLANATION

The given parabola has equation:

[tex] {y}^{2} - 4x - 8y - 12 = 0[/tex]

[tex] {y}^{2} - 8y = 4x +12[/tex]

Complete the square for the quadratic equation in y.

[tex]{y}^{2} - 8y + {( - 4)}^{2} = 4x + 12 + {( - 4)}^{2} [/tex]

[tex]{y}^{2} - 8y + {( - 4)}^{2} = 4x + 12 + 16[/tex]

[tex]{( y- 4)}^{2} = 4x + 28[/tex]

[tex]{( y- 4)}^{2} = 4(x +7)[/tex]

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

alinakincsem

Answer:

(-7, 4)

Step-by-step explanation:

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

[tex] y ^ 2 - 4 x - 8 y - 1 2 = 0 [/tex]

[tex]y^2-(\frac{8}{2} )^2-4x-12=(\frac{8}{2} )^2\\[/tex]

[tex] y ^ 2 - 1 6 - 4 x - 1 2 = 1 6 [/tex]

[tex] ( y - 4 ) ^ 2 - 4 x - 1 2-16=0[/tex]

[tex](y-4)^2=4x+28[/tex]

[tex](y-4)^2=4(x+7)[/tex]

[tex]x+7=0, y-4=0[/tex]

x = -7, y = 4

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