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Published byAllyson Bell Modified over 5 years ago

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Solving Quadratic Equaitons Section 3.1 beginning on page 94

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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.

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

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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.

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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)

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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.

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

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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

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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

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Solving a Multi-Step Problem

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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

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Practice

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