Question

Need help with this math question

Answer 1

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:

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

$y^2-(\frac{8}{2} )^2-4x-12=(\frac{8}{2} )^2$

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

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

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

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

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

x = -7, y = 4

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

Answer 2

ANSWER

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)