Final answer:
To find the y-intercept of the equation y=-2x³ +3x² +1, we set x=0 and simplify to find that the y-intercept is the point (0,1).
Step-by-step explanation:
To determine the y-intercept of the curve defined by the equation y=-2x³ +3x² +1, we can set the value of x to zero, since the y-intercept is where the curve crosses the y-axis (the vertical axis), and this occurs at x=0. Upon substituting x with zero, we simplify the equation to y=-2(0)³ + 3(0)² + 1, which equals 1. Thus, the y-intercept is 1, which means the curve crosses the y-axis at the point (0,1).