Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

Define a polynomial function.

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is the difference between a rational and an irrational number?

Back

A rational number can be expressed as a fraction a/b where a and b are integers and b ≠ 0. An irrational number cannot be expressed as a simple fraction, and its decimal representation is non-repeating and non-terminating.

Front

Explain the concept of a function.

Back

A function is a relation that assigns exactly one output for each input from a set of inputs. It can be represented as f(x), where x is the input.

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.

Front

How do you find the x-intercepts of a quadratic function?

Back

To find the x-intercepts of a quadratic function, set the function equal to zero and solve for x using factoring, completing the square, or the quadratic formula.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots of a quadratic equation: if it's positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

Front

Define a linear equation.

Back

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.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness and is calculated as the change in y divided by the change in x (rise/run).

Front

Explain the concept of a system of equations.

Back

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