Final answer:
To determine the quadratic function that passes through (-2,22), (1,-5), and (3,-3), you first plug the points into the standard quadratic equation, then solve the resulting system of equations to find the specific values of a, b, and c that define the function.
Step-by-step explanation:
To find the quadratic function that includes the points (-2,22), (1,-5), and (3,-3), we need to solve a system of equations based on the general form of a quadratic function, which is f(x) = ax² + bx + c. We will plug each point into this equation to form a system of three equations that can be solved simultaneously to find the values of a, b, and c.
For the point (-2,22), the equation is: 22 = a(-2)² + b(-2) + c. For the point (1,-5), the equation is: -5 = a(1)² + b(1) + c. For the point (3,-3), the equation is: -3 = a(3)² + b(3) + c.
By solving this system of equations, we can determine the coefficients a, b, and c that define the quadratic function.