(a)

The vertex form of a quadratic equation is y = a(x - p)² + q where (p, q) are the x- and y-coordinates of the vertex

vertex is (1, -4) and y- intercept is 2.

vertex (1, -4) is lies on parabola.So substitute p = 1 , q = -4 y = a(x - (-4))² + 1

y = a(x + 4)² + 1 y- intercept is 2.y-intercept is at (0, 2),Hence given equation further becomes 2 = a(0 + 4)² + 1

16a  = 2 - 1 a = 1/16 Therefore, the quadratic equation is: y = (1/16)(x + 4)² + 1