Answer:
y = 2x³-6x²-2x +6
Explanation:
You want the equation of a graph with two turning points, and x-intercepts at -1, +1, and +3. The y-intercept is 6.
Factors
Each x-intercept of x=p means the equation has a factor of (x -p). This means the factored equation will be ...
y = a(x +1)(x -1)(x -3) = a(x² -1)(x -3) = a(x³ -3x² -x +3)
y-Intercept
The y-intercept is 3a = 6, so a = 2 and the function is ...
y = 2x³ -6x² -2x +6