The parent function f(x) = x² is a parabola that opens upwards, with its vertex at the origin (0, 0). When we apply the transformation h(x) = -f(x), it results in a new function that reflects the graph of f(x) across the x-axis and then flips it vertically.
Specifically, for any input value x, the output value of -f(x) will be the negative of the corresponding output value of f(x). This means that the transformation will invert the y-values of f(x), effectively reflecting the graph across the x-axis. Then, the negative sign in front of f(x) will flip the reflected graph vertically, resulting in a downward opening parabola.
Therefore, the transformed function h(x) = -f(x) will be a parabola that opens downwards with its vertex at the origin. The shape of the parabola will be the same as the parent function f(x) = x², but it will be flipped and inverted.