- single variable equations
- systems of linear-quadratic and quadratic-quadratic equations in two variables.
[C, CN, PS, R, T, V]
(a) | $ \text "Note: It is intended that the quadratic equations be limited to those that correspond to quadratic functions."$ |
(b) |
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. |
(c) |
Derive the quadratic formula, using deductive reasoning. |
(d) |
Apply strategies for solving quadratic equations of the form $ax^2 + bx + c = 0$ including:
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(e) |
Explain different strategies for verifying the solution to a quadratic equation. |
(f) |
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. |
(g) |
Apply knowledge of quadratic equations and functions to identify and correct any errors within a solution to a quadratic equation. |
(h) |
Solve situational questions involving the writing and solving of quadratic equations. |
(i) |
Match systems of linear-quadratic and quadratic-quadratic functions to situations. |
(j) |
Develop, generalize, explain, and apply strategies for solving systems of linear-quadratic and quadratic-quadratic functions, including:
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(k) |
Explain the meaning of the intersection point of a system of linear-quadratic or quadratic-quadratic equations in terms of the situation being modeled. |
(l) |
Illustrate and explain how a system of linear-quadratic or quadratic-quadratic equations may have zero, one, two, or an infinite number of solutions. |
(m) |
Solve situational questions by using systems of linear-quadratic or quadratic-quadratic equations. |