Big Idea:

Big Idea 2

Quadratic functions have 0, 1, or 2 real roots.

1 week

Evidence of Understanding

  • solve a quadratic equation using any method  
    • construct viable arguments to justify a solution method and articulating assumptions
      • describe the process for finding the solution (NOT proving why the solution is correct)
    • solve a quadratic equation for one variable in terms of another variable (x in terms of y, etc.)
    • use a graph to determine and approximate the solutions to a quadratic equation
      • describe how the graph visually represents values that make the equation true
      • recognize d = ax2 + bx + c has solutions where f(x) = ax2 + bx + c intersects with f(x) = d
      • connect the factors with roots of a polynomial equation and the x intercepts on its graph
      • Example: solutions to 5 = x2 + 2x - 3 are x values where y = x2 + 2x - 3 meets the line y = 5
    • estimate and justify reasonable and unreasonable solutions
      • Example:  For 10 = x2 + 2x - 3, recognize numbers larger than 5 are not reasonable solution options because squaring 5 and adding more to it will be much higher than 10
    • discuss advantages and disadvantages of different methods that arise (some examples might be strategically guessing and checking, using a graph or table, working backwards, etc.)

 

  • solve a quadratic equation in vertex form using an algebraic method
    • justify how each step maintains the equation’s balance
    • determine the solution set and classify solutions as real, complex, rational, or irrational
      • express a square root in simplest form by factoring out perfect squares
      • fluently add, subtract, multiply, or divide rational and irrational numbers
    • describe the conditions of a quadratic equation that generate 0, 1, or 2 real roots
      • use the values of a, h, and k to determine when the roots of the function will be real, complex, rational, irrational, equal, and/or unequal  

 

Develop conceptual understanding:

roots, solution, factor, zero product property, inverse operation, real, complex

Supporting terms to communicate:

function, quadratic, parabola, equation, solution set, standard form, vertex form, factored form, perfect square, difference of squares, square root, vertex, x intercept, rational, irrational, equal

Core Resource
A core resource supports multiple days of instruction. COMING SOON!