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WARM UP What do you remember?...

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QUADRATIC EQUATIONS SECTION 5.5

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OBJECTIVES By the end of this part of the lesson, you should be able to… Simplify square roots. Solve quadratic equations by finding square roots.

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SOLVING QUADRATIC EQUATIONS WITH SQUARE ROOTS If a quadratic equation is missing the b term we can solve using square roots. The goal is to get x by itself.

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EXAMPLE 1: SIMPLIFYING RADICALS

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EXAMPLE 2: SIMPLIFYING RADICALS

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EXAMPLE 4: SOLVING BY FINDING SQUARE ROOTS Step 1) Rewrite in form ax 2 = c. Step 2) Isolate x 2. Step 3) Simplify. Step 4) Take the square root of each side.

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EXAMPLE 5: SOLVING BY FINDING SQUARE ROOTS

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EXAMPLE 6: SOLVING BY FINDING SQUARE ROOTS

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OBJECTIVES By the end of today, you should be able to… Solve quadratic equations by factoring and graphing. What does it mean to solve an equation? Quick Review: When you solve an equation, you’re finding the values that make the statement true.

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QUADRATIC EQUATIONS Remember - the standard form of a quadratic equation is ax 2 + bx + c = 0, where a ≠ 0. You can solve some quadratic equations in standard form by factoring the quadratic expression and then using… The Zero-Product Property!

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THE ZERO-PRODUCT PROPERTY The Zero-Product Property helps us solve quadratic equations that have been factored. The Zero-Product Property states: If ab = 0, then a = 0 or b = 0. For example, if (x + 3)(x - 7)=0, then (x + 3) = 0 or (x - 7) = 0.

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EXAMPLE 1: SOLVING BY FACTORING Solve by factoring. Step 1) Write in standard form. Step 2) Factor. Step 3) Use the Zero-Product Property. Step 4) Solve for x.

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EXAMPLE 2: SOLVING BY FACTORING Solve by factoring. Step 1) Write in standard form. Step 2) Factor. Step 3) Use the Zero-Product Property. Step 4) Solve for x.

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EXAMPLE 3: SOLVING BY FACTORING Solve by factoring. Step 1) Write in standard form. Step 2) Factor. Step 3) Use the Zero-Product Property. Step 4) Solve for x.

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EXAMPLE 4: SOLVING BY FACTORING Solve by factoring. Step 1) Write in standard form. Step 2) Factor. ???

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SOLVING BY GRAPHING You can solve a quadratic equation in standard form by graphing its related quadratic function, y = ax 2 + bx +c and finding the x-intercepts. Quadratic equation cannot be solved by factoring Quadratic equation can be solved by graphing!

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SOLVING BY GRAPHING 1)Write in standard form 2)Graph in your calculator 3)Find the x-intercepts

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SOLVING BY GRAPHING EquationX-intercept(s) x 2 – 6x + 9 x 2 + 4x – 5

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HOMEWORK Worksheet 5.5 #s 1, 3, 7, 11, 30, 34, 53, 60 Systems Projects – due Monday!

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