Adv. Algebra Final Exam Review Part I

Front

What is the vertex of the function f(x) = (x-1) - 5?

Back

(1,-5)

Front

What is the result of adding the complex numbers -9 + 6i and 15i?

Back

6i

Front

What is the standard form of a quadratic function?

Back

f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you find the vertex of a quadratic function in vertex form?

Back

The vertex is given by the point (h, k) in the function f(x) = a(x-h)^2 + k.

Front

What is the discriminant in a quadratic equation and what does it indicate?

Back

The discriminant is b^2 - 4ac; it indicates the nature of the roots (real and distinct, real and equal, or complex).

Front

What is the formula for the sum of the roots of a quadratic equation?

Back

The sum of the roots is -b/a.

Front

What is the formula for the product of the roots of a quadratic equation?

Back

The product of the roots is c/a.

Front

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

Back

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a simple fraction.

Front

What is the definition of 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.

Front

What is the process of factoring a quadratic expression?

Back

Factoring involves expressing the quadratic in the form (x - p)(x - q) where p and q are the roots.