Final answer:
The dilation factor of the function y = 5x² is determined by the coefficient of the x² term, which is 5. Hence, the correct answer is A: 5.
Step-by-step explanation:
The function y = 5x² represents a parabola that is stretched vertically away from the x-axis. The dilation factor of this function is determined by the coefficient of the x² term. Since the coefficient is 5, that is our dilation factor. In general terms, if we have a function y = kx², the number k is what affects the stretch or compression of the parabola. If k is greater than 1, the graph stretches, whereas if k is between 0 and 1, the graph is compressed.
The dilation factor here does not consider the sign; it only reflects the absolute value of the stretch or compression, hence a negative factor would still represent dilation, albeit with a reflection across the x-axis. The dilation factor of a quadratic function is determined by the coefficient of the squared term. In this case, the function is y = 5x². Since the coefficient of the squared term is 5, the dilation factor is 5.
Therefore, for the function y = 5x², the correct answer is A: 5.