Christina Maggio Grades 10th -12th October 21, 2012 Quadratic Equations Christina Maggio Grades 10th -12th October 21, 2012

Students will learn how to graph quadratic functions. Quadratic Equations Students will learn how to solve quadratic equations by factoring, completing the square, and by using the quadratic formula. Students will learn how to graph quadratic functions. Students will use graphing calculators to find approximate solutions. We will be learning how to solve quadratic equations using factoring, completing the square and by plugging the numbers into the quadratic formula. After that we will learn how to graph quadratic equations. Don’t worry it only sounds scary.

Here is a short video to get you thinking about what we will be learning.

How to Solve a Quadratic equation Factoring Completing the square Using the quadratic formula In the video there were examples of factoring , completing the square and using the quadratic formula.

Factoring The first step is to set the equation equal to zero. Then you find the numbers that are factors of the second term and add up to the last term. Next you make two mini equations each equal to zero. Finally solve each mini equation for X. Factoring factoring quadratics

Completing the Square Start with the quadratic in general form. Move the constant to the other side of the equation. Factor out the “a” value. Add 𝑏 2 2 to the trinomial inside the brackets. Solve for X. ***Remember with an equation what you do to one side you have to do to the other*** completing the square

IF THEN Quadratic Formula This may look intimidating but it is just plugging numbers in!! quadratic formula

Is this a quadratic equation? How do you know if an equation is a quadratic equation? A quadratic equation is always going to have an “x” squared in it. And that x squared will be the variable with the largest exponent.

Graphing Quadratic equations These are the things you will use and to look for when graphing a quadratic equation. You will enter the equation in the spot that says y equals after you do that you push the graph button, the calculator will graph it. Then you look at where the graph crosses the x axis. This is the solution to the quadratic equation. It is still important to solve the equation with pencil and paper though because on a calculator you cannot see the exact answer just an approximation. It is a good way to check your work.

Game Time!!! Ok now it is time for a review to see what you have learned. I want the class to split up into groups of six and to pull out one piece of paper and a pencil per group. I am going to give you six different quadratic equations, two at a time and you are going to have to solve each one. The first two you are to use factoring to solve. When you group has come up with an answer you are to raise you hand. When I see your hand raise one person from each team will come up to the board and work the problem out showing all steps. Then a different person from the group will come up and do the other problem. We will do this for all six problems. The second two quadratic equations must be solved by completing the square, and the last two will be solved by using the quadratic formula. After we have done all six on the board you will turn your group paper in with all six equations done correctly on it with all group members names on the paper. For each correct problem you team will earn 1 point of extra credit on the chapter test next week. There will be six equations and six people per group each of you must come up to the board and do one problem.

Factoring!!!

Completing the squares

Quadratic Formula!!!

Resources http://www.youtube.com/watch?v=jGJrH49Z2ZA&feature=related http://www.youtube.com/watch?v=OFSrINhfNsQ http://www.mathsisfun.com/algebra/quadratic-equation.html http://www.youtube.com/watch?v=GyCuj1hx_zc http://www.youtube.com/watch?v=s80J2dAUUyI