Evidence of Understanding

**create equivalent quadratic equations or expressions and justify equivalency**- create area models that represent any quadratic equation using a square
*Example: use algebra tiles to represent y = x*^{2}+ 2x + 5 and reorganize the tiles into a square with “leftover” tiles to create an area model equivalent to y = (x + 1)^{2}+ 4

- express an equation from standard form to vertex form using
**perfect squares***Example: y = x*^{2 }+ 2x + 5 is equivalent to y = (x^{2}+ 2x + 1) + 4 and y = (x + 1)^{2}+ 4

- describe how a, b and c values of standard form are related to h and k of vertex form

- create area models that represent any quadratic equation using a square

**solve a quadratic equation in standard form using an algebraic method**- determine solutions by factoring and applying the
**zero product property**- recognize when a quadratic equation is factorable or not factorable and explain why
- describe the property of multiplication in which when ab = 0 either a = 0 or b = 0 and use it to solve a quadratic equation in factored form

- find solutions for an equation in standard form by
**completing the square** - describe how the
**quadratic formula**relates to completing the square*possible extension: derive the quadratic formula by completing the square for y = ax*^{2}+ bx + c

- identify a, b, and c values from the standard form and substitute them into the quadratic formula to determine solutions

- determine solutions by factoring and applying the

**analyze quadratic equations to justify a solution method**- solve a quadratic equation using multiple methods and compare advantages of each method
- substitute the solution to show the equation is true
- create criteria for determining which solution method is most efficient
*Example: when b is odd it is more difficult to complete the square, when a or b are decimals it is easier to use the quadratic formula, etc.*

- prove solutions can be determined using different methods that produce equivalent results

Develop conceptual understanding:

completing the square, square, quadratic formula, discriminant

Supporting terms to communicate:

quadratic, parabola, roots, solution, solution set, standard form, factored form, factor, vertex form, perfect square, term, coefficient, inverse operation, square root, real, complex, rational, irrational, equal, axis of symmetry, vertex, x intercept