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 = ax
^{2}+ bx + c has solutions where f(x) = ax^{2}+ 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 = x*^{2}+ 2x - 3 are x values where y = x^{2}+ 2x - 3 meets the line y = 5

- estimate and justify reasonable and unreasonable solutions
*Example: For 10 = x*^{2}+ 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.)

- construct viable arguments to justify a solution method and articulating assumptions

**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