Algebra 2 Final

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

How do you find the zeros of a polynomial equation?

Back

To find the zeros of a polynomial equation, set the equation equal to zero and solve for the variable. For example, for (x+10)(x-2) = 0, the zeros are x = -10 and x = 2.

Front

What is the distance formula?

Back

The distance formula is used to find the distance between two points (x1, y1) and (x2, y2) in a coordinate plane: d = √((x2 - x1)² + (y2 - y1)²).

Front

How do you simplify square roots?

Back

To simplify square roots, factor the number under the root into its prime factors and look for pairs. For example, √45 = √(9*5) = √9 * √5 = 3√5.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation ax² + bx + c = 0: x = (-b ± √(b² - 4ac)) / (2a).

Front

What does it mean for a function to be quadratic?

Back

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

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. It can be found using the formula (-b/(2a), f(-b/(2a))).

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express the equation in the form (x - p)(x - q) = 0, where p and q are the roots. Then set each factor to zero: x - p = 0 or x - q = 0.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

What is a linear inequality?

Back

A linear inequality is an inequality that involves a linear function. It can be written in the form ax + b < c, ax + b > c, etc., and represents a region on a graph.