Answer:
2x^2 + 2x + 10 = 0
Explanation:
f(x) = 2x^2 + 2x + 10
This equation is derived using the standard form of a quadratic function f(x) = ax^2 + bx + c. By substituting the coordinates of the given points into the equation, a system of three equations is formed. Solving this system yields the coefficients a, b, and c, which are found to be a = 2, b = 2, and c = 10.
- The coefficient a = 2 indicates a concave upward parabolic curve, reflecting a positive quadratic term.
- The coefficient b = 2 influences the slope and direction of the curve as it governs the linear term.
- The constant term c = 10 represents the y-intercept, the point where the curve intersects the y-axis.