Final answer:
To find the quadratic function based on the given points, we set up a system of equations using the general form of a quadratic function and solve for the coefficients a, b, and c.
Step-by-step explanation:
The given points (-2,8), (0,4), and (4,68) are to be used to find the quadratic function that fits them. A quadratic function has the form f(x) = ax^2 + bx + c. We can find the values of a, b, and c by creating a system of equations using the given points and then solving for a, b, and c.
For the first point (-2,8), the equation is: a(-2)^2 + b(-2) + c = 8.
For the second point (0,4), the equation is: 4 = c because any value of x multiplied by 0 will be 0.
For the third point (4,68), the equation is: a(4)^2 + b(4) + c = 68.
Plugging in the values, we get:
1) 4a - 2b + c = 8
2) c = 4
3) 16a + 4b + c = 68
Next, substitute c = 4 into the first and third equations and solve the system for a and b. Once we find a, b, and c, we will have the quadratic function that passes through the given points.