Final answer:
The maximum value of the quadratic equation y = 1 - x² is 1. This maximum can be found by determining the vertex of the parabola, which occurs when x = 0, giving us y = 1. The correct answer is b) 1.
Step-by-step explanation:
The student has asked to find the maximum value of the quadratic equation y = 1 - x². This equation represents a downward-opening parabola with its vertex as the highest point on the graph. To find the maximum value, we need to determine the y-coordinate of the vertex.
For any quadratic equation in the form y = ax² + bx + c, the x-coordinate of the vertex can be found using the formula -b/(2a). Since the given equation is y = 1 - x² or y = -1·x² + 0·x + 1, a = -1 and b = 0. Plugging these values into the formula, we find the x-coordinate to be -0/(2·-1) = 0.
Substituting x = 0 into the original equation to find the maximum y-value, we get y = 1 - (0)² = 1. Therefore, the maximum value of y for the equation y = 1 - x² is 1, which corresponds to option b).