Big Idea:

Big Idea 3

Quadratic equations can be solved by rearranging the equation into an equivalent form.

1 week

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 = x2 + 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+ 2x + 5 is equivalent to y = (x2 + 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 

 

  • 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 = ax2 + bx + c
    • identify a, b, and c values from the standard form and substitute them into the quadratic formula to determine solutions

 

  • 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

Core Resource

A core resource supports multiple days of instruction.

  • Completing the Square
    Students are introduced to completing the square and the quadratic formula and make connections between these two processes for solving quadratic equations and their corresponding quadratic functions.
    Resource:
    Completing the Square

    Students are introduced to completing the square and the quadratic formula and make connections between these two processes for solving quadratic equations and their corresponding quadratic functions.

    All Resources From: