quadratics - copied
quadratic equation
The highest exponent on the variable is a 2. The standard form is ax² + bx + c = 0.
constant term
a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constants. If it is not a constant it is called a variable.
vertex form
a quadratic function is given by. f (x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.
completing the square
a technique used to solve quadratic equations, graph quadratic functions, and evaluate integrals. This technique can be used when factoring a quadratic equation does not work or to find irrational and complex roots.
linear term
an algebraic equation in which each term is either a constant or the product of a constant
rational roots
any time b² -4a > 0 or = to 0
discriminant
expression under the radical in the quadratic formula.
quadratic term
graphed as a parabola. f(x)= ax^2 + bx + c
vertex
highest or lowest point of a line of parabola.
axis of symmetry
highest/lowest point on a parabola. -b over 2a
roots
if the equation equals zero.
quadratic formula
is used in algebra to solve quadratic equations (polynomial equations of the second degree). The general form of a quadratic equation is , where x represents a variable, and a, b, and c are constants, with . A quadratic equation has two solutions, called roots.
square root property
one method that is used to find the solutions to a quadratic (second degree) equation. This method involves taking the square roots of both sides of the equation. Before taking the square root of each side, you must isolate the term that contains the squared variable.
irrational roots
the value that was squared to make 2 (ie the square root of 2) cannot be a rational number.
complex roots
A given quadratic equation ax 2 + bx + c = 0 in which b 2 -4ac < 0 has two complex roots: x = , . Therefore, whenever a complex number is a root of a polynomial with real coefficients, its complex conjugate is also a root of that polynomial.