Solving Quadratic Equaitons Section 3.1 beginning on page 94

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.

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

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.

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)

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.

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

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

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

Solving a Multi-Step Problem

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

Practice