Enduring understandings of quadratic relationships ESSENTIAL QUESTIONS AND QUADRATICS REVIEW

 Function, relation, domain, range, perfect square trinomial, difference of perfect squares, roots/zeroes, real and complex roots, extrema, minimum, maximum, y-intercept, line or Axis of symmetry, standard form, vertex form, intercept form, 1 st difference, 2 nd difference, completing the square, the discriminant, quadratic formula VOCABULARY

What are the forms of a quadratic function and what are the benefits of each?

Standard? Vertex? Factored or Intercept form?

What is the fundamental theorem of algebra and how does it relate to quadratic functions? How do a visual and an algebraic model demonstrate the theorem? How does the discriminant help you understand where the roots will be?

How does a quadratic data table compare to other types of functions? Where is evidence that a function is quadratic on a table, graph, and equation?

Second Differences? Highest power on x? Parabola?

How do algebraic manipulations of a function highlight different features? How do algebraic techniques like completing the square and the quadratic formula help to highlight key features of a quadratic function?

How do transformations of the parent function y = x^2 create changes on the graph and how does this relate to families of quadratics?

How do roots, both real and imaginary, help in writing functions?

PRACTICE QUESTIONS

 Graph and note all key features PRACTICE QUESTIONS

 Determine a function that creates these roots PRACTICE QUESTIONS

 Determine the function that has the following roots and produces the point (0, 50) – Careful! PRACTICE QUESTIONS

 How can the geometric understanding of parabolas help us to connect algebra and geometry?

 Given the diagram below, determine an equation that represents this parabola.