Solving Quadratic Equations by Finding Square Roots

43210 In addition to level 3, students make connections to other content areas and/or contextual situations outside of math. Students will factor polynomials using multiple methods, perform operations (excluding division) on polynomials and sketch rough graphs using key features. - Factor using methods including common factors, grouping, difference of two squares, sum and difference of two cubes, and combination of methods. - Add, subtract, and multiply polynomials, - Explain how the multiplicity of the zeros provides clues as to how the graph will behave. - Sketch a rough graph using the zeros and other easily identifiable points. Students will factor polynomials using limited methods, perform operations (excluding division) on polynomials, and identify key features on a graph. - Add and subtract polynomials. - Multiply polynomials using an area model. - Factor polynomials using an area model. - Identify the zeros when suitable factorizations are available. - Identify key features of a graph. Students will have partial success at a 2 or 3, with help. Even with help, the student is not successful at the learning goal. Focus 9 Learning Goal – ( HS.A-SSE.A.1, HS.A-SSE.A.2, HS.A-SEE.B., HS.A-APR.A.1, HS.A- APR.B.3, HS.A-REI.B.4) = Students will factor polynomials using multiple methods, perform operations (excluding division) on polynomials and sketch rough graphs using key features.

Remember: Linear equation is x to the first power ax+by=c Quadratic equation: is x to the second power Standard Form: ax 2 +bx+c=0

Find Solutions to ax 2 +c=0 (Get x 2 alone in form x 2 =d) Once you get x 2 =d take the square root of both sides to get x.

3 Results 1. x 2 =d If d is a positive number, then you have 2 solutions 2. x 2 =d If d=0 then there is only one solution x=0 3. x 2 =d If d is a negative number, there is no solution (Can’t take sq. root of a negative)

Examples: 2. x 2 = x 2 =4 x can be + or -, when squared it is positive 2

Solve: 4x = x 2 = -100 (divide both sides by 4) x 2 = -25 NO Solution

3x = 0 3x 2 = 99 x 2 = 33 Two Solutions

The surface area of a cube is 150ft 2. Find the length of each edge. x x x SA = 6s = 6s 2 1st DIVIDE BY 6 25 = s 2 Sides of the cube are 5 ft. You can’t have a negative length.

Watch out below! A construction worker on the top floor of a 200 foot tall building accidentally drops a heavy wrench. How many sections will it take to hit the ground? The formula d=rt is used when the speed is constant. However, when an object is dropped, the speed continually increases. Use the formula: h = -16t 2 + s h = final height of object t = time s = starting height of object h = -16t 2 + s 0 = -16t = -16t = t 2 √12.5 = t About 3.54 seconds.