Question

Function upper A is a concave up parabola. The curve passes through left parenthesis negative 2 comma 4 right parenthesis and through left parenthesis 2 comma 4 right parenthesis, with the function's minimum point at left parenthesis 0 comma 0 right parenthesis. Function B is also a concave up parabola, and passes through left parenthesis negative 4 comma 4.5 right parenthesis, left parenthesis negative 2 comma 2 right parenthesis, left parenthesis 0 comma 0.5 right parenthesis, left parenthesis 2 comma 0 right parenthesis, and left parenthesis 4 comma 0.5 right parenthesis. The 2 curves intersect at left parenthesis negative 1.1 comma 1.1 right parenthesis and at left parenthesis 0.5 comma 0.25 right parenthesis. Values are approximate.

Describe the transformations from Function A
to Function B
.

(1 point)

narrower and shifted right 2 units

wider and shifted left 2 units

narrower and shifted left 2 units

wider and shifted right 2 units

Answer 1

Wider and shifted right 2 units.

A: y = x^2 (vertex (0,0)). B: using (4,0.5) gives y = a(x−2)^2 and 4a = 0.5 ⇒ a = 1/8, so B = (1/8)(x−2)^2. The vertex moved right 2, and the coefficient 1/8 < 1 makes it wider.