Presentation on theme: "Solving Quadratic Equations by the Quadratic Formula"— Presentation transcript:
1 Solving Quadratic Equations by the Quadratic Formula
2 THE QUADRATIC FORMULA This is the quadratic formula! Just identify a, b, and c then substitute into the formula.
3 WHY USE THE QUADRATIC FORMULA? The quadratic formula allows you to solve ANY quadratic equation, even if you cannot factor it.An important piece of the quadratic formula is what’s under the radical:b2 – 4acThis piece is called the discriminant.
4 WHY IS THE DISCRIMINANT IMPORTANT? The discriminant tells you the number and types of answers(roots) you will get. The discriminant can be +, –, or 0which actually tells you a lot! Since the discriminant isunder a radical, think about what it means if you have apositive or negative number or 0 under the radical.
5 WHAT THE DISCRIMINANT TELLS YOU! Value of the DiscriminantNature of the SolutionsNegative2 imaginary solutionsZero1 Real SolutionPositive – perfect square2 Reals- RationalPositive – non-perfect square2 Reals- Irrational
6 Example #1 a=2, b=7, c=-11 Discriminant = Discriminant = Find the value of the discriminant and describe the nature of the roots (real,imaginary, rational, irrational) of each quadratic equation. Then solve the equation using the quadratic formula)1.a=2, b=7, c=-11Discriminant =Value of discriminant=137Positive-NON perfect squareNature of the Roots – 2 Reals - IrrationalDiscriminant =
7 Example #1- continuedSolve using the Quadratic Formula
8 Solving Quadratic Equations by the Quadratic Formula Try the following examples. Do your work on your paper and then check your answers.