Final answer:
The y-intercept of the polynomial equation y = x⁴ - 3x³ - 2x² + 6x² is found by evaluating the equation at x = 0, which gives a result of 0. Therefore, the correct y-intercept is D.(0,0).
Step-by-step explanation:
The student's question is about finding the y-intercept of the polynomial equation y = x⁴ - 3x³ - 2x² + 6x². The y-intercept of an equation is the y-value where the graph of the equation intersects the y-axis (where x = 0). To find the y-intercept of the given polynomial, we need to evaluate the equation for x = 0.
Substituting x = 0 into the equation, we get:
y = (0)⁴ - 3(0)³ - 2(0)² + 6(0)² = 0
Every term in this equation becomes zero because they all contain the factor x raised to some power. Hence, the y-intercept of the equation is 0. According to the options provided, the correct answer is D.(0,0).