Algebra: Concepts and Connections EOC Review 2

A triangle is a right triangle if the square of the length of the longest side is equal to the sum of the squares of the lengths of the other two sides (Pythagorean theorem).

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

A rational number is any number that can be expressed as the quotient or fraction $$\frac{p}{q}$$ of two integers, where $$q \neq 0$$ .

An irrational number is a number that cannot be expressed as a simple fraction; its decimal representation is non-repeating and non-terminating.

The product of a rational number and an irrational number is always irrational.

A linear function is a function that can be graphically represented as a straight line, described by the equation $$f(x) = mx + b$$ , where m is the slope and b is the y-intercept.

A quadratic function is a polynomial function of degree 2, typically written in the form $$f(x) = ax^2 + bx + c$$ .

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola (opening upwards or downwards).

The perimeter of a fenced area can be determined by adding the lengths of all sides of the shape.

The distance between two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is given by the formula $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ .