Review Function Forms

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

Front

How do you find the average rate of change of a function between two points?

Back

The average rate of change between two points (x1, f(x1)) and (x2, f(x2)) is given by (f(x2) - f(x1)) / (x2 - x1).

Front

What does it mean to combine like terms in algebra?

Back

Combining like terms means to simplify an expression by adding or subtracting terms that have the same variable raised to the same power.

Front

What is the difference between standard form and vertex form of a quadratic function?

Back

Standard form expresses the function as f(x) = ax^2 + bx + c, while vertex form expresses it as f(x) = a(x-h)^2 + k, highlighting the vertex.

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

How do you convert from standard form to vertex form?

Back

To convert from standard form to vertex form, you can complete the square.

Front

What is 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 n is a non-negative integer.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.