Key+Characteristics+of+Quadratics

Students will:
 * Unit Goal:** Solve quadratic equations in one variable. **A.REI.4**
 * 1) solve quadratic equations by inspection.
 * 2) solve quadratic equations by taking square roots.
 * 3) solve quadratic equations by completing the square.
 * 4) solve quadratic equations by factoring.
 * 5) solve quadratic equations using the quadratic formula.
 * 6) recognize when the quadratic formula gives complex solutions.
 * 7) write complex solutions as a ± //bi// for real numbers a and b.

__**//First Learning Cycle//**__ Goal is to find the square roots and investigate perfect squares. The objectives we will concentrate on are:
 * 1.** Students will explore square roots


 * //Develop://**

__Launch:__ Have students determine the area of square photos, or other square objects. Then try to determine the side length using trial and error when the area of an object is known.

__Explore:__ **//equation 1: h = -16t//****//2//** **//+ 256//** **//equation 2: h = -16t//****//2//** **//+ 324//** 1. The height //h// (in feet) of a ball dropped from the top of a building can be modeled by the given equation 1 where //t// is the time (in seconds). Use factoring to find the time it takes for the ball to hit the ground, or when h = 0.

2. Solve the equation 1 when //h = 0// for //t////2////.// Ask the students to find which number times itself is 16.

3. The height //h// ( in feet) of a ball dropped from another building can be modeled by equation 2. Can you use find the time it takes for the ball to hit the ground? Explain.

4. Solve equation 2 when //h = 0// for //t////2// //.// Use trial and error to find the time it takes for the ball to hit the ground.

__Discuss:__
 * Remind students to always use the symbol ± to solve these problems to emphasize the need to take both the positive and negative roots.