Evidence of Understanding

**determine and describe the key characteristics about a quadratic from its equation**- analyze characteristics of a quadratic equation whose graph has 0, 1, or 2 real roots
- predict the features of the roots of a parabola by analyzing its quadratic equation

- use the quadratic formula to describe patterns with the
**discriminant**that cause the quadratic to have 0, 1, or 2 real roots- classify the roots as real, complex, rational, irrational, equal, and/or unequal

- describe strategies for identifying the vertex and axis of symmetry from a quadratic written in vertex, standard, or factored form
- recognize the axis of symmetry is always the
**average**of the roots - explain why -
^{b}/_{2a}as the axis of symmetry for a quadratic function and use it to determine the coordinates of the vertex

- recognize the axis of symmetry is always the

- analyze characteristics of a quadratic equation whose graph has 0, 1, or 2 real roots

**generate quadratic function models and use them to solve problems**- accept or reject solutions using the constraints in a situation
- construct and justify an equation, table, graph, situation, or verbal description relating inputs and outputs given any representation of the quadratic function
- analyze values to justify a quadratic function model (and not linear or exponential)
- recognize quantitative relationships between variables to create a polynomial in one variable, Example: express the product of three consecutive numbers as x(x + 1)(x + 2)
- given a point stated as the vertex and any other point, determine the function rule
- possible extension: given the y intercept and two other points on the quadratic, create a system of equations to solve for the values of a, b, and c and find the quadratic equation

- solve a system of equations (linear/quadratic,exponential/quadratic, quadratic/quadratic), identify solutions graphically or algebraically, and justify the solution(s) in terms of a situation.

Supporting terms to communicate:

equivalent, function, equation, quadratic, parabola, solution, solution set, standard form, factored form, factor, vertex form, perfect square, completing the square, quadratic formula, discriminant, term, coefficient, inverse operation, square root, real, complex, rational, irrational, equal, roots, intercepts, vertex, axis of symmetry, domain, range, discrete, continuous