1. Determine the form of the function: determine the form of the function according to the information given in the title, that is, determine the values of A, B and C.
2. Solving vertex coordinates: The vertex coordinates of a quadratic function can be obtained by the formula x = -b/(2a). Substituting this x value into the function, you can get the corresponding y value and get the vertex coordinates (x, y).
3. Solve the discriminant: The discriminant can be used to judge the intersection of the image of the function and the X axis, that is, the number of roots. The formula of the discriminant is δ = b 2-4ac, where there are two unequal real roots when δ is greater than 0, two equal real roots when δ is equal to 0, and no real roots when δ is less than 0.
4. Solving the value of X: According to the requirements of the topic, the value of X can be solved by discriminant. When the discriminant is positive, find two real roots with the root formula X = (-b√δ)/(2a); When the discriminant is zero, use the formula x = -b/(2a) to find the root.
As for why A plus B equals 1, this is because the standard form of a quadratic function with one variable is f (x) = ax 2+bx+c, where A and B are coefficients of the function and c is a constant term. The values of a and b can be determined according to specific problems. It is a special case that their sum is equal to 1, and not all unary quadratic functions meet this condition.
I hope it helps you.