- vertex
- domain and range
- direction of opening
- axis of symmetry
- x- and y-intercepts.
[CN, ME, PS, R, T, V]
| (a) |
Generalize a rule from sets of graphs, using inductive reasoning, and explain about how different values of a (including 1, 0, and -1) transform the graph of $y = ax^2. |
| (b) |
Generalize a rule from sets of graphs, using inductive reasoning, and explain about how different values of q (including 0) transform the graph of $y = x^2 + q$. |
| (c) |
Generalize a rule from sets of graphs, using inductive reasoning, and explain how different values of p (including 0) transform the graph of $y = (x - p)^2$. |
| (d) |
Develop, generalize, explain, and apply strategies for determining the coordinates of the vertex, the domain and range, the axis of symmetry, x- and y- intercepts, and direction of opening of the graph of the function $f(x) = a(x-p)^2 + q$ without the use of technology. |
| (e) |
Develop, explain, and apply strategies for graphing functions of the form $f(x) = a(x - p)^2 + q$ by applying transformations related to the values of a, p, and q. |
| (f) |
Develop, explain, and apply strategies (that do not require graphing or the use of technology) for determining whether a quadratic function will have zero, one, or two x-intercepts. |
| (g) |
Develop, explain, and apply strategies for writing a quadratic function in the form of $y = a(x - p)^2 + q$ that represents a given graph or set of characteristics of a graph. |
| (h) |
Develop, generalize, explain, verify, and apply a strategy (including completing the square) for writing a quadratic function in the form $y = ax^2 + bx + c$ in the form $y = a(x - p)^2 + q$. |
| (i) |
Using knowledge about completing the square, identify and correct errors in a given example of completing the square. |
| (j) |
Develop, generalize, explain, and apply strategies for determining the coordinates of the vertex, the domain and range, the axis of symmetry, x- and y- intercepts, and direction of opening of the graph of a function in the form $y = ax^2 + bx + c$. |
| (k) |
Sketch the graph of a quadratic function given in the form $y = ax² + bx + c$. |
| (l) |
Write a quadratic function that models a given situation and explain any assumptions made. |
| (m) |
Analyze quadratic functions (with or without the use of technology) to answer situational questions. |
