If the graph of the quadratic function h is shifted vertically 3 units upward, then reflected in the x-axis, and then shifted horizontally 5 units to the left, the resulting graph is the parabola f(x) = x2. What is the rule of the function h?

Question

anonymous · Answer

I'm going to assume that by "rule of h(x)" you mean the equation:
If f(x) is shifted 3 up, then h(x) + 3. Reflected on the x-axis, -(h(x) + 3). Shifted horizontal 5 left  is -h(x+5) +3.
$$h(x) =-(x +5) ^{2} + 3$$

ps. I'm assuming f(x) = x2 means x squared

anonymous · Answer

actually the correct answer is $$-(x-5)^{2}-3$$