Retake Semester 1 Final Exam: Algebra 2

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that returns the non-negative value of a number, defined as f(x) = |x|. It reflects all negative values of x to positive values.

Front

How do you find the inverse of a function?

Back

To find the inverse of a function, swap the x and y variables in the equation and solve for y. The inverse function undoes the action of the original function.

Front

What is the factored form of the trinomial x² - 8x + 15?

Back

The factored form is (x - 5)(x - 3).

Front

What is the process for subtracting polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements, meaning each output is produced by exactly one input.

Front

What is the 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 determine 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 ax² + bx + c = 0.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value).

Front

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

Back

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