Final answer:
To write a quadratic equation that contains the points (0,3), (2,9), and (4,-1), substitute the x and y values of the points into the general form of a quadratic equation and solve for the coefficients. The resulting quadratic equation is y = -1.9x^2 + 5.4x + 3.5.
Step-by-step explanation:
To write a quadratic equation that contains the points (0,3), (2,9), and (4,-1), we can use the general form of a quadratic equation, which is y = ax^2 + bx + c. By substituting the x and y values of the given points into the equation, we can solve for the coefficients a, b, and c. Using the points (0,3), (2,9), and (4,-1), we get the equations:
0a + 0b + c = 3
4a + 2b + c = 9
16a + 4b + c = -1
Simplifying the equations and solving the system of equations, we find that a = -1.9, b = 5.4, and c = 3.5. Therefore, the quadratic equation is y = -1.9x^2 + 5.4x + 3.5.