Question

Kevin says that the graph of the function f(x) = -(x - 2)2 + 3 is a parabola that opens downward and has a vertex at (3, 2). Complete the explanation describing Kevin's error. Kevin is ______that the graph is a parabola that open vertex is at ( , )

Answer 1

Kevin made a mistake in identifying the vertex of the parabola. The graph of the function f(x) = -(x - 2)2 + 3 is a downward opening parabola with the vertex at (2, 3), not (3, 2).

Step-by-step explanation:

Kevin is incorrect that the graph of the function f(x) = -(x - 2)2 + 3 has a vertex at (3, 2).

The correct form of the function is a parabola that opens downward, as indicated by the negative sign before the squared term. To find the vertex, we set the inside of the squared term equal to zero. In this case, x - 2 = 0, which implies x = 2. Substituting x = 2 back into the function, we get f(2) = -(2 - 2)2 + 3 = 3. Therefore, the vertex of the parabola is actually at (2, 3), not (3, 2).