Evidence of Understanding

**describe connections between a polynomial equation and the features of its graph**- correlate the equation’s
**degree**to the maximum number of real**roots**and end behavior - distinguish a minimum or maximum point as
**absolute**or**relative**using a function’s degree - generalize how the equation’s lead coefficient impacts the graph’s direction and rate of change
- classify a function as
**odd**,**even**or neither from*both*the equation*and*its graph- analyze examples and nonexamples including polynomial, absolute value, trigonometric, rational, exponential, logarithmic, and radical functions
- describe how the graphs of even or odd functions reflect in the coordinate plane
- explain why the equation for an odd function cannot have a constant term

- correlate the equation’s
**investigate and and determine specific features of a parabola and its quadratic equation**- study various forms of a quadratic equations (factored, standard, vertex) to understand why a quadratic function has at most two real zeros
*possible extension: show how the degree limits a quadratic to at most 2 real zeros*

- explore how the
**axis of symmetry**relates to roots, the**vertex**, and other points on the parabola- justify why the vertex always lies on the axis of symmetry
- use the axis of symmetry to explain why the vertex is located in the middle of the roots, and is the only point with an unrepeated output value

- approximate the roots of a given parabola and verify them using its quadratic equation
- use the degree to classify roots as real or imaginary
- connect characteristics of the roots with characteristics of the quadratic equation

- predict and justify the end behavior of a quadratic equation using its degree and lead coefficient

- study various forms of a quadratic equations (factored, standard, vertex) to understand why a quadratic function has at most two real zeros

Develop conceptual understanding:

polynomial, degree, roots, zeros, absolute, relative, odd, even, quadratic, cubic, quartic, axis of symmetry, vertex

Supporting terms to communicate:

lead coefficient, exponent, reflect, minimum, maximum, end behavior, vertex form, standard form, factored form