NC Math 3 Unit 1-4 Review

Front

What is a function in mathematics?

Back

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

Front

Define the term 'quadratic function'.

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.

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, set the function equal to zero and solve for x using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

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

Front

Explain the concept of 'discriminant' in a quadratic equation.

Back

The discriminant is the part of the quadratic formula under the square root (b² - 4ac) that 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 equation?

Back

A linear equation is an equation of the first degree, which means it can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

Define 'slope' in the context of a linear function.

Back

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

Front

What is the difference between a rational function and a polynomial function?

Back

A rational function is a ratio of two polynomials, while a polynomial function is a sum of terms with non-negative integer exponents.

Front

How do you determine if a relation is a function?

Back

A relation is a function if each input has exactly one output. This can be checked using the vertical line test on its graph.