SOLVE QUADRATIC EQUATIONS

Lessons & Objectives:

Solving Quadratic Equations: Factoring

• Solve problems by rewriting quadratic equations in standard form and factoring, pointing out the solutions that are viable or not viable in a modeling context.

• Write a quadratic equation that models a scenario.

Solving Quadratic Equations: Square Root Property

• Use the square root property to solve quadratic equations.

Solving Quadratic Equations: Completing the Square

• Solve a quadratic equation whose leading coefficient is 1 by completing the square.

• Solve a quadratic equation whose leading coefficient is greater than 1 by completing the square.

Introduction to the Quadratic Formula

• Justify the steps used to derive the quadratic formula by completing the square.

• Recognize an expression that uses the quadratic formula to find the solutions of a quadratic equation.

• Determine the values of a, b, and c from a given quadratic equation in standard form.

• Relate the discriminant in the quadratic formula to the types of solutions of a quadratic equation.

Solving Quadratic Equations: Quadratic Formula

• Determine the number of real zeros of a quadratic function by finding the values of a, b, and c, and then calculating the discriminant.

• Solve a quadratic equation using the quadratic formula.

Modeling with Quadratic Equations

• Write and solve quadratic equations to model real-world scenarios, estimating where appropriate and identifying solutions that are not viable in terms of the context.

Solving Linear-Quadratic Systems

• Solve a system of equations consisting of a line and a parabola algebraically and graphically, using technology where appropriate.