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 does the vertex form of a quadratic function look like?

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 x=a and x=b is given by (f(b) - f(a)) / (b - a).

Front

What is the significance of the leading coefficient in a polynomial function?

Back

The leading coefficient determines the end behavior of the polynomial function and whether it opens upwards or downwards.

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 a_n, a_{n-1}, ..., a_0 are constants and n is a non-negative integer.

Front

What is the difference between linear and quadratic functions?

Back

Linear functions have a constant rate of change and are represented by a straight line, while quadratic functions have a variable rate of change and are represented by a parabola.

Front

What does it mean to combine like terms in algebra?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power.

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 convert from vertex form to standard form?

Back

To convert from vertex form f(x) = a(x-h)^2 + k to standard form, expand the equation and simplify to the form f(x) = ax^2 + bx + c.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b^2 - 4ac, and it determines the nature of the roots.