Algebra 2 Review

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

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 the direction it opens. For the quadratic function f(x) = ax² + bx + c, the vertex can be found at the point (h, k) where h = -b/(2a) and k = f(h).

Front

How do you find the roots of a quadratic equation?

Back

The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a). The expression under the square root, b² - 4ac, is called the discriminant.

Tags

CCSS.HSA-REI.B.4B

Front

What is the discriminant and what does it indicate?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It indicates the nature of the roots: if it's positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Tags

CCSS.HSA-REI.B.4B

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 (f(x) = mx + b), while quadratic functions have a variable rate of change and are represented by a parabola (f(x) = ax² + bx + c).

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into simpler components (factors) that, when multiplied together, give the original expression. For example, x² - 5x + 6 can be factored into (x - 2)(x - 3).

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. This form makes it easy to identify the vertex and the direction of opening.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables raised to whole number powers and coefficients. It can be expressed in the form P(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0.

Front

What is the difference between a monomial, binomial, and trinomial?

Back

A monomial is an algebraic expression with one term (e.g., 3x), a binomial has two terms (e.g., x + 2), and a trinomial has three terms (e.g., x² + 3x + 2).

Front

What is the process of completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q. This involves manipulating the equation to form a perfect square trinomial.

Tags

CCSS.HSA-REI.B.4B