Final answer:
To find the quadratic function that satisfies the given conditions, we can use the x-intercepts and a point to set up a system of equations and solve for the coefficients.
Step-by-step explanation:
To find the quadratic function that satisfies the given conditions, we can start by writing the general form of a quadratic function: y = ax^2 + bx + c. Since we know that the function passes through the point (5,8), we can substitute these values into the equation and solve for a, b, and c: 8 = a(5)^2 + b(5) + c
Next, we can use the x-intercepts (-3,0) and (4,0) to set up two additional equations:
0 = a(-3)^2 + b(-3) + c
0 = a(4)^2 + b(4) + c
Solving this system of equations, we find that a = 1/7, b = -1/7, and c = 77/7. Therefore, the quadratic function that satisfies the given conditions is y = (1/7)x^2 - (1/7)x + 11.