chp 2 vocab

completing the square

the process of adding (b/2)² to x² + bx to form a perfect-square trinomial.

complex conjugates

complex numbers with equivalent real parts and opposite imaginary parts are complex conjugates

complex number

numbers that can be written in the form of a+bi, where a and b are real numbers and i is the square root of -1

discriminant

the value of the expression b² - 4ac from a quadratic equation in standard form. The value of it determines the number of solutions of the equation

imaginary number

any number of the form bi, where b is a nonzero real number and i is the square root of -1

imaginary unit i

the complex number whose square root is -1

Parabola

the graph of a quadratic function. It is the set of all points P in a plane that are the same distance from a fixed point F, the focus, as they are from line d, the directrix

quadratic equation

x= (-b ± √(b² - 4ac)) / (2a) for ax² + bx +c = 0 with a ≠ 0

quadratic function

a function that you can write in the form of 𝑓(𝑥) = 𝑎𝑥² + 𝑏𝑥 + 𝑐 with 𝑎 ≠ 0

standard form of a quadratic function

f(x)= ax² + bx + c with 𝑎 ≠ 0

vertex form of a quadratic function

f(x)= a(x-h)² + k, where 𝑎 ≠ 0 and ( h , k ) is the vertex of the function

zero product property

if the product of two or more factors is zero, then at least one of the factors must be zero