Final answer:
To find the equation, substitute the given points into the equation and solve for the coefficients. The equation of the quadratic function is y = -0.5x^2 + 4x + 4.5.
Step-by-step explanation:
To find the equation of the quadratic function, we can substitute the given points into the equation and solve for the coefficients a, b, and c. Let's start with the point (1, 4).
Substituting x=1 and y=4 into the equation y = ax2 + bx + c, we get 4 = a(1)2 + b(1) + c. Simplifying this equation gives us a + b + c = 4.
Similarly, substituting the other two points, we get two more equations: 1 = 4a + 2b + c and 4 = 9a + 3b + c. Now we have a system of three equations that we can solve to find the values of a, b, and c.
After solving the system of equations, we find that a = -0.5, b = 4, and c = 4.5. Therefore, the equation of the quadratic function is y = -0.5x2 + 4x + 4.5.