1. Solving Quadratic Equaitons Section 3.1 beginning on page 94

2. The Big Ideas In this section we will solve quadratic equations in three different ways. Solve By Graphing: Use the graphing calculator to find the x-intercepts (which are the solutions to the equation) Solve Using Square Roots: When the variable appears only once we can isolate what is being squared and find the solutions using square roots. Solve By Factoring: When the equation is factorable, we can use the zero product property to find the solutions to the quadratic. Previous Knowledge: Properties of Square Roots Factoring Simplifying Radicals Rationalizing Denominators Core Vocabulary: Quadratic Equation in One Variable Root of an Equation Zero of a Function

3. Solving By Graphing Enter into your graphing calculator as is. Find the x-intercepts (zeros)

4. Radical Review Simplifying Radicals: If the radicand had a perfect square factor, factor it out and simplify it. Rationalizing The Denominator: If the denominator has a radical in it, multiply the numerator and the denominator by that radical.

5. Solving Using Square Roots Step 1: Get what is being squared alone Step 2: Find the square root of both sides. Simplify the radical if possible Be sure to account for BOTH solutions ** No Real Solutions (The square of a real number cant be negative)

6. Step 1: Get what is being squared alone Step 2: Find the square root of both sides. Simplify the radical if possible, be sure to account for BOTH solutions Rationalize the denominator (if necessary) Step 3: Get x alone.

7. Zero Product Property This property is why we use factoring to solve quadratic equations (when they are factorable)

8. Solving a Quadratic Equation By Factoring Get everything to one side Factor Set each factor equal to zero and solve -45  -4 1,-45 3,-15 5,-9

9. Finding the Zeros of a Quadratic Function 24  -11 -1,-24 -2,-12 -3,-8 Set equal to zero Factor Use the zero product property

10. Solving a Multi-Step Problem

11. Continued… To find the maximum, find the y-value of the vertex (section 2.2) To maximize revenue each subscription should cost $22 (20 + x) and the maximum revenue would be $968,000

12. Practice