Which equation represents the axis of symmetry of the function y = -2x² + 4x - 6?
y = 1, x = 1, x = 3, x = -3

Solution:

Given function is y = -2x² + 4x - 6

The axis of symmetry is the line that divides the parabola into two identical halves. It passes through the vertex of the parabola.

To find the axis of symmetry we have to convert the equation to (x - h)² = 4a (y - k)² form.

⇒ y = -2x² + 4x - 6

(y + 6) = -2x² + 4x

(y + 6) = -2(x² - 2x)

(y + 6) = -2(x² - 2x + 1 - 1)

(y + 6) = -2{(x - 1)² - 1}

(y + 6) = -2(x - 1)² + 2

-2(x - 1)² = (y + 4)

⇒ (x - 1)² = -1/2 (y + 4)

Therefore, the axis of symmetry is x = 1.

Which equation represents the axis of symmetry of the function y = -2x² + 4x - 6?

Summary:

The axis of symmetry of the function y = -2x² + 4x - 6 is x = 1.