Objectives
 Write the general form of the quadratic formula and state its use.
 State the conditions that must be met to use the quadratic formula.
 Identify equations that can be solved using the quadratic formula.
 Use the quadratic formula to find the solutions to a quadratic equation.
 Define the discriminant and state what it tells about the solutions to the equation.
 Apply the quadratic formula to find the roots of a quadratic equation.
 Use the discriminant to determine how many roots a polynomial has.
Key Terms
 Complex Numbers – The set of all numbers of the form a + bi, where a and b are any real numbers and i equals .
 Discriminant – The number under the radical sign in the quadratic formula. It is given by the expression .
 Imaginary Number – The square root of a negative number. The imaginary number i is defined as the square root of –1.
 You can use to find the square root of any negative number.
 Quadratic Formula – A formula used to solve quadratic equations.
 The solutions to the quadratic equation are given by the formula .
 Radical – A term that has the form where b can be a number, a variable, or an expression that contains both.
 The symbol indicates the nth root.
 The symbol (no n) indicates a square root.
 Roots – Values for which a function equals zero.
 The roots are also called zeros of the function.
 Any xvalue at which the graph of a function crosses the xaxis is a root of the function.
Notes
Deriving the Quadratic Formula 


Solving Quadratic Equations 




Discriminants and Complex Numbers 
Roots 
