Lesson 5: 3-6 The Quadratic Formula and the Discriminant
Duration of Days: 4
Lesson Objective
1. Solve quadratic equations by using the Quadratic Formula.
2. Use the discriminant to determine the number and type of roots of a quadratic equation.
1. How can you generalize the pattern of all quadratic equations?
2. What part of the quadratic formula relates to the axis of symmetry?
3. What part of the quadratic formula determines the type of the solutions to the quadratic equation?
4. What types of solutions are possible?
5. How can you use b^2-4ac to decide what type of solution to expect?
Quadratic Formula
Discriminant
N.CN.7 Solve quadratic equations with real coefficients that have complex solutions.
A.SSE.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.
SAT questions related to solving quadratics: 2-3-13,3-3-14,1-3-16,5-3-3,8-3-16,1-4-25; analyzing graphs: 3-4-12,8-3-11,8-4-19,6-3-11
Any quadratic written in the form ax^2+bx+c=0, where a does not equal zero, can be solved using the Quadratic Formula.
Pumpkin catapult is an event in which a contestant builds a catapult and launches a pumpkin at a target. The path of the pumpkin can be modeled by quadratic function h=-4.9t^2+117t+42, where h is the height of the pumpkin and t is the number of seconds. To predict when the pumpkin will hit the target, you can solve the equation 0=-4.9t^2+117t+42. This equation would be difficult to solve using factoring, graphing, or completing the square, so using the Quadratic Formula is a good method.
Some students may have commented that some of the equations could have been solved by factoring. Stress that many quadratic equations cannot be solved easily by factoring. Emphasize that the Quadratic Formula provides a way to find the roots for any quadratic equation.
Remind students that conjugate pairs are two complex numbers of the form a+bi and a-bi.
Encourage students to write down the values of a, b, and c from the standard form of the quadratic equation before they begin substituting them into the formula.
Have students research the root words that form the words quadratic and discriminant. Discuss how the root words relate to the mathematical meanings of quadratic and discriminant.
McGraw Hill resources
McGraw Hill resources