Final answer:
To find a quadratic function that includes the set of values (0,8), (2,18), and (3,17), we can use the given values to set up a system of equations and solve for the coefficients of the quadratic function. We can then write the quadratic function using the values of a, b, and c.
Step-by-step explanation:
To find a quadratic function that includes the set of values (0,8), (2,18), and (3,17), we can use the general form of a quadratic function, which is y = ax^2 + bx + c. Substituting the given values, we can set up a system of equations to solve for the coefficients a, b, and c. Using the quadratic formula, we can find the solutions for the quadratic function.
Let's substitute the values (0,8) into the equation:
8 = a(0)^2 + b(0) + c
This simplifies to c = 8.
Next, let's substitute the values (2,18) into the equation:
18 = a(2)^2 + b(2) + 8
This simplifies to 4a + 2b = 10. (1)
Finally, substitute the values (3,17) into the equation:
17 = a(3)^2 + b(3) + 8
This simplifies to 9a + 3b = 9. (2)
We now have a system of equations (1) and (2). We can solve this system to find the values of a and b, and then substitute these values back into the equation to find c. Once we have a, b, and c, we can write the quadratic function.