Question

Let P2(x)= a₁x²+a₂x+a₃. Use the direct evaluation method, which involves substituting xi and yi values to obtain a system of equations for the coefficients ai, to determine the specific working and expressions for a₁, a₂ and a₃ inP₂(x).

Answer 1

The direct evaluation method involves substituting xi and yi values to obtain a system of equations for the coefficients ai in the polynomial function P2(x) = a₁x² + a₂x + a₃. To determine the specific values for a₁, a₂, and a₃, we can substitute three known points (xi, yi) into the equation and solve the resulting system of equations.

Step-by-step explanation:

The direct evaluation method involves substituting xi and yi values to obtain a system of equations for the coefficients ai in the polynomial function P2(x) = a₁x² + a₂x + a₃. To determine the specific values for a₁, a₂, and a₃, we can substitute three known points (xi, yi) into the equation and solve the resulting system of equations. For example, if we have three points (x₁, y₁), (x₂, y₂), and (x₃, y₃), we can substitute these values into the equation and obtain the following system of equations:

a₁x₁² + a₂x₁ + a₃ = y₁

a₁x₂² + a₂x₂ + a₃ = y₂

a₁x₃² + a₂x₃ + a₃ = y₃

We can then solve this system of equations to find the values of a₁, a₂, and a₃.