Unit+10


 * Unit 10**

In Unit 10 we learn about Quadratic equations and how to solve them in a multitude of ways. The first thing that we must know about quadratics is that, when they are graphed they form what is called a "parabola". That's a U-shape. Sometimes the U is right-side up, other times, it is upside-down. Quadratics are generally in the form y=ax 2 +bx+c When solving quadratics you must have the quadratic equation set equal to 0. ax 2 +bx+c=0. We can solve quadratics in 4 different ways:1. By factoring and setting each factor equal to 0. We learned factoring in Unit 9. I suggest that you go back and look at the Unit 9 page if you forget how to factor. Here is an example. 2. By using square roots. Remember that to "undo" a squared term you must square root, and when taking a square root, you get two solutions- a positive and negative solution. This only works when your quadratic is a binomial or a binomial squared. Note: the positive and negative 3 as the solutions.

3. By completing the square. A useful technique to learn especially to find the vertex of the parabola quickly. You'll learn more about this in Algebra 2. A few simple steps to create a Perfect Square Trinomial. 1. Move constant term. 2. Cut b-term in half and square it. 3. Add to both sides. 4. Factor the PST-should be a binomial squared. 5. Square root both sides. Don't forget the + and the - 6. Add or subtract. The last way we learn to solve a quadratic is by using the Quadratic Formula. To use the formula you must identify the a, b, and c, coefficients from the quadratic equation in standard form. Remember that it must be equal to 0 to solve. Once you identify a,b, and c, you plug them into the formula:That will give you two solutions. What do the solutions to quadratics give us? Well...they tell us the values of x where y=0. Graphically, that is where the parabola crosses the x-axis. The DISCRIMINANT tells us how many times the parabola crosses the x-axis. if b 2 -4ac<0, then it never crosses. If b 2 -4ac=0 then it touches at one point. If b 2 -4ac>0 then it crosses twice. Take a look at the graphs below. Which is which? The notes on from Unit 10 can be downloaded here.

Graphing parabolas is an important thing to know how to do. The notes on how to graph three points on the parabola can be downloaded here. There's also a practice page on solving and graphing quads with square roots here. Notes for __Solving Quadratics with Square Roots__ and __Completing the Square__:

The notes on the Solving using the Quadratic Formula can be downloaded here

At the end of the unit we practice some more "completing the square" and using the "Quadratic Formula" on this worksheet.