Find the sum of a + b if the graph of the function y = x ^ 2 + ax + b passes through the points M (-1.7) and N (2.4).

If the graph of the function y = x² + a * x + b passes through the points M (-1; 7) and N (2; 4), then the coordinates of these points must satisfy the equation of this function, in other words, the following equalities must be satisfied: 7 = (-1) ² + a * (-1) + b and 4 = 2² + a * 2 + b. Rewriting these equalities –а + b = 6 and 2 * а + b = 0 we obtain a system of two linear equations for two unknowns а and b. Let us express b in terms of a. We have: b = a + 6 and b = -2 * a. Therefore, a + 6 = -2 * a or a + 2 * a = -6, whence a = -6: 3 = -2. Therefore, b = -2 + 6 = 4. Answer: a = -2 and b = 4.