Since the shown parabola opens upward, the coefficient of x2 in the equation y=ax2+c must be positive. Given that a is positive,−a is negative, and therefore the graph of the equation y=a(x−b)2+c will be a parabola that opens downward. The vertex of this parabola is (b, c), because the maximum value of y, c, is reached when x = b. Therefore, the answer must be choice B.Choices A and C are incorrect. The coefficient of x2 in the equation y=−a(x−b)2+c is negative.Therefore, the parabola with this equation opens downward, not upward. Choice D is incorrect because the vertex of this parabola is (b,c), not (−b,c), because the maximum value of y,c, is reached when x=b.