Section 9.1 The Square Root Property Section 9.2 The Quadratic Formula.

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Presentation transcript:

Section 9.1 The Square Root Property Section 9.2 The Quadratic Formula

Overview Recall that a quadratic equation is in the form Up to this point, we have solved quadratic equations by factoring…

The Problem? Although every quadratic equation has at least one solution, not every quadratic equation will factor…

The Square Root Property The big idea: Given (something) 2 = a number: 1.Take the square root of both sides (the square root and the squared exponent will cancel each other out, leaving just the radicand. 2.Don’t forget the “plus or minus” 3.Simplify the radical 4.Isolate the variable

Examples

The Quadratic Formula Can be used on any quadratic equation (even the ones that will factor).

Steps In The Process 1.Make sure your equation is in the right form. 2.Identify a, b, and c. Substitute them into the formula. 3.Watch your signs! 4.When you square a negative, you get a positive. I don’t care what your calculator says. 5.Simplify the radical. 6.Be careful when you reduce (all three places, all by the same factor, or not at all).

Examples

Summary of Solving Quadratic Equations If you can factor it, factor it. Then set each factor equal to zero. If you can’t factor it, or if it won’t factor, use the quadratic formula. If it comes to you in the form (something) 2 = a number do not unravel it. Use the square root property.