Algebra 2 Review

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens. For the function f(x) = ax² + bx + c, the vertex can be found at the point (h, k) where h = -b/(2a) and k = f(h).

The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a). The expression under the square root, b² - 4ac, is called the discriminant.

The discriminant is the part of the quadratic formula under the square root, b² - 4ac. It indicates the nature of the roots: if it's positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

A linear equation is an equation of the first degree, meaning it can be written in the form ax + b = 0, where a and b are constants and a ≠ 0. Its graph is a straight line.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept, the point where the line crosses the y-axis.

A system of equations is a set of two or more equations with the same variables. Solutions to the system are the values of the variables that satisfy all equations simultaneously.

The method of substitution involves solving one equation for one variable and then substituting that expression into the other equation to find the values of the variables.

The method of elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output. It can be represented as f(x).