Question

Find the equation of the parabola which is symmetric about the y - axis and passes through the point (2,–3).

Answer 1

This parabola also passes through (-2, -3).

y = -(x - h)² + k

-3 = -(2 - h)² + k

-3 = -(2 + h)² + k

0 = -(2 + h)² + (2 - h)²

0 = -(4 + 4h + h²) + 4 - 4h + h²

0 = -4 - 4h - h² + 4 - 4h + h²

h = 0

y = -x² + k

-3 = -(-2)² + k

-3 = -4 + k

k = 1

y = -x² + 1