Unpacking the Outcome
Demonstrate understanding

quadratic equations
 single variable equations
 linear-quadratic systems

quadratic-quadratic systems
Outcome (circle the verb and underline the qualifiers)
P20.8 Demonstrate understanding of quadratic equations including the solution of:
• single variable equations
• systems of linear-quadratic and quadratic-quadratic equations in two variables.
BE ABLE TO DO a. Explain, using examples, the relationship among the roots of a quadratic equation, the zeros of the corresponding quadratic function and the x-intercepts of the graph of the quadratic function.
KNOW
Vocabulary: quadratic equation, root(s) of an equation, zero(s) of an equation, extraneous root, quadratic formula, discriminant, systems of linear-quadratic or quadratic-quadratic equations
UNDERSTAND
That each quadratic equation is related to a graph of a quadratic function, each with a unique shape.
Quadratic equations, when graphed, have a parabolic shape.
Quadratic equations can have zero, one or two real roots.
That the discriminant can be used to predict the number of roots.
That decimal roots are an approximation.
That there exists multiple ways to solve quadratic equations, some more convenient than others, depending upon the quadratic itself.
That the points of intersection of graphs represent the solution to the system.
Systems may have none, one or two real solutions. b. Derive the quadratic formula, using deductive reasoning. c. Apply strategies for solving quadratic equations of the form ax² + bx + c = 0 including:
• determining square roots
• factoring
• completing the square
• applying the quadratic formula
• graphing its corresponding function, with and without the use of technology. d. Explain different strategies for verifying the solution to a quadratic equation. e. Explain, using examples, how the discriminant may be used to determine whether a quadratic equation has two, one, or no real roots; and relate this knowledge to the number of zeros that the corresponding quadratic function will have. f. Apply knowledge of quadratic equations and functions to identify and correct any errors within a solution to a quadratic equation. g. Solve situational questions involving the writing and solving of quadratic equations. h. Match systems of linear-quadratic and quadratic-quadratic functions to situations. i. Develop, generalize, explain, and apply strategies for solving systems of linear-

quadratic and quadratic-quadratic functions, including:
• graphically
• algebraically
• with the use of technology. j. Explain the meaning of the intersection point of a system of linear-quadratic or quadratic-quadratic equations in terms of the situation being modeled. k. Illustrate and explain how a system of linear-quadratic or quadratic-quadratic equations may have zero, one, two, or an infinite number of solutions. l. Solve situational questions by using systems of linear-quadratic or quadraticquadratic equations.
ESSENTIAL QUESTIONS
How can we determine the number of roots of a quadratic equation?
How can we derive the quadratic formula?
What is the best method for solving a given quadratic equation?
What can we learn from the discriminant?
What is the meaning of the intersection point in the system of equations?
What is the best method for solving the system of equations?