NC MATH 3 EOC REVIEW 3

Front

What is the quadratic formula?

Back

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

Front

Define a function. Give an example.

Back

A function is a relation that assigns exactly one output for each input. Example: f(x) = 2x + 3 is a function where for each value of x, there is a unique value of f(x).

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has the form f(x) = mx + b, where m and b are constants, and its graph is a straight line. A quadratic function has the form f(x) = ax² + bx + c, where a ≠ 0, and its graph is a parabola.

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 the direction it opens. For the quadratic function f(x) = ax² + bx + c, the vertex can be found at x = -b/(2a).

Front

Explain the concept of slope in a linear equation.

Back

The slope of a linear equation represents the rate of change of the dependent variable with respect to the independent variable. It is calculated as the rise over run (change in y over change in x).

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It is expressed as a² + b² = c².

Front

Define the term 'asymptote'.

Back

An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or oblique.

Front

What is the difference between independent and dependent variables?

Back

An independent variable is the variable that is changed or controlled in an experiment, while a dependent variable is the variable that is measured or affected in response to changes in the independent variable.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations in the system.

Front

Explain the concept of a limit in calculus.

Back

A limit is a fundamental concept in calculus that describes the value that a function approaches as the input approaches a certain point.