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Name:__________ warm-up 4-3 Use the related graph of y = –x 2 – 2x + 3 to determine its solutions Which term is not another name for a solution to a quadratic equation? A. zero B.x-intercept C.root D.vertex Use the related graph of y = x 2 – 4 to determine its solutions.

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Solve –2x 2 + 5x = 0. If exact roots cannot be found, state the consecutive integers between which the roots are located. Use a quadratic equation to find two real numbers that have a sum of 5 and a product of –14.

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Details of the Day EQ: How do quadratic relations model real-world problems and their solutions? Depending on the situation, why is one method for solving a quadratic equation more beneficial than another? How do transformations help you to graph all functions? Why do we need another number set? I will be able to… Write quadratic equations in intercept form. Solve equations of the form x 2 + bx + c = 0 by factoring. Activities: Warm-up Review homework Notes: 4-3 solving quadratic equations Class work/ HW Vocabulary: quadratic equation factored form FOIL method

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S4-3 Solving Quadratic equations by Factoring Factoring *** Factoring *** Factoring *** Factoring *** Factoring *** Factoring ***Quadratic Equations Factoring *** Factoring ***

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A Quick Review Use the related graph of y = x 2 – 4 to determine its solutions. Use the related graph of y = –x 2 – 2x + 3 to determine its solutions Which term is not another name for a solution to a quadratic equation? A. zero B.x-intercept C.root D.vertex

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A Quick Review Solve –2x 2 + 5x = 0. If exact roots cannot be found, state the consecutive integers between which the roots are located. Use a quadratic equation to find two real numbers that have a sum of 5 and a product of –14.

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Notes and examples (x – p)(x – q)=0Write the pattern Replace p with ½ and q with –5 Simplify. Use FOIL Get rid of fractions

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Notes and examples

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Solve 9y 2 + 3y = 0. Solve y 2 = 36

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Notes and examples Solve x 2 – 16x + 64 = 0. Solve 5x 2 + 34x + 24 = 0

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Notes and examples Solve 6x 2 – 5x – 4 = 0Factor 3s 2 – 11s – 4.

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Notes and examples ARCHITECTURE The entrance to an office building is an arch in the shape of a parabola whose vertex is the height of the arch. The height of the arch is given by h = 9 – x 2, where x is the horizontal distance from the center of the arch. Both h and x are measured in feet. How wide is the arch at ground level? To find the width of the arch at ground level, find the distance between the two zeros 9 – x 2 =0 Original expression Multiply both sides by –1.

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Notes and examples TENNIS During a match, Andre hit a lob right off the court with the ball traveling in the shape of a parabola whose vertex was the height of the shot. The height of the shot is given by h = 49 – x 2, where x is the horizontal distance from the center of the shot. Both h and x are measured in feet. How far was the lob hit?

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