Question

what is the axis of symmetry of y=-4(x+8)^2-6.

Answer 1

Given parabola y = - 4(x + 8)^2 - 6.

Write in standard form of parabola y = ax ^2 + bx + c..

y = - 4(x ^2 + 16x + 64) - 6

  = - 4x ^2 - 64x - 256 - 6

y = - 4x ^2 - 64x - 262.

Compare it with standard  form of parabola y = ax ^2 + bx + c.

a = - 4, b = - 64, and c = - 262.

Axis of symmetry x = - b / 2a.

Substitute a = - 4, b = - 64 in x = - b / 2a .

x = - (- 64)/2 * (- 4)

  = 64/- 8

  = - 8.

Therefore, axis of symmetry of y = - 4(x + 8)^2 - 6 is - 8.

Answer 2

The function is y = - 4(x + 8)² - 6.

The above equation represent the standard form of the equation of parabola.

The standard form of the parabola with vertex (h, k) and axis of symmetry x = h is y = a(x - h)² + k.

Compare the equation y = - 4(x + 8)² - 6 with standard form of the parabola : y = a(x - h)² + k.

Vertex : (h, k) = (- 8, - 6) and the axis of symmetry : x = h = - 8.