Evidence of Understanding

**create a table of values or graph from an explicit or recursive rule and use it to solve problems**- graph a parabola from the factored, standard, or vertex form of its equation and label its vertex and intercepts (approximately for non-integer values)
- strategically use technology to determine the scale and orientation of a parabola in the coordinate plane

- create a table of values that highlights key characteristics of a quadratic function including its vertex, intercepts, and
**symmetry** - find and justify
**domain**and**range**values for a quadratic from its graph, table, and equation*Example: evaluate f(x) = 5 by looking at the graph or table, or find f(3) by looking at the graph, table, or by calculating the value using the rule*- justify whether a given point is on a parabola, given its equation
- explore and justify why the domain of a quadratic function contains all real numbers

- describe how the graph of any equation visually represents values that make the equation true
- describe the solution set of a quadratic function from its graph

- graph a parabola from the factored, standard, or vertex form of its equation and label its vertex and intercepts (approximately for non-integer values)

**construct an explicit or recursive function rule from an equivalent representation**- describe how quantities from a situation, sequence, or table, or points on a graph map to parts of the factored, standard, or vertex form of a quadratic equation
- explain why both representations are equivalent
- describe advantages and disadvantages of different representations for a function

- create and justify a quadratic equation in factored, standard, or vertex form given a situation, sequence, table or graph
- Example: create f(x) = (x - 1)
^{2}or f(x) = x^{2}+ 3 and describe the relationship between quantities in the function rule with the situation, table, sequence, or graph that it models - use the
**rate of change**to create and justify a**recursive**rule for a quadratic function

- Example: create f(x) = (x - 1)

- describe how quantities from a situation, sequence, or table, or points on a graph map to parts of the factored, standard, or vertex form of a quadratic equation

***NOTE: algebraic conversion between forms of a quadratic equation is part of Unit 6**

Develop conceptual understanding:

parent function, transformation, reflection, translation, dilation

Supporting terms to communicate:

function, quadratic, parabola, domain, range, independent, dependent, input, output, axis of symmetry, vertex, maximum, minimum, root, intercept, rate of change, interval, vertex form, coefficient