The value of b for the quadratic equations is 3.
How to solve the quadratic function?
The quadratic function f(x) = ax² + bx + c passes through the points (-1,25), (3,21), and (4,50).
To find the value of b, we can use the fact that the x and y coordinates of each point satisfy the equation f(x) = ax² + bx + c.
Substituting the coordinates of the first point, we get 25 = a(-1)² + b(-1) + c, which simplifies to a - b + c = 25.
Substituting the coordinates of the second point, we get:
21 = a(3)² + b(3) + c, which simplifies to:
9a + 3b + c = 21.
Substituting the coordinates of the third point, we get:
50 = a(4)² + b(4) + c, which simplifies to:
16a + 4b + c = 50.
We now have a system of three equations in three variables:
a - b + c = 25
9a + 3b + c = 21
16a + 4b + c = 50.
Solving this system, we get a = -2, b = 3, and c = 20.
Therefore, the value of b is 3.