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BELL-WORK

This sketch shows the graph of the quadratic equation y = -6x^2 + 12x + 18, including its x-intercepts, axis of symmetry, vertex, and y-intercept.

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BELL-WORK

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  1. BELL-WORK Sketch the graphof y = -6x2 + 12x + 18. y = -6(x + 1)(x – 3) x-intercepts: (-1,0),(3,0) AOS: x = -12 2(-6) x = 1 Vertex: x = 1 y = -6(1)2 + 12(1) + 18 y = 24 (1,24) y-intercept: y = -6(0)2 + 12(0) + 18 y = 18 (0,18) SKETCH

  2. Square Root When ever the square root symbol is used, there will be two results: the principal root (the positive square root) and a negative root. If you introduce the square root to a problem, you must give both roots! Solve the equation by finding square roots. n2 = 81 n = +√81 n = +9

  3. Solving Quadratic Equations Solve the equation by using square roots. k2 – 196 = 0 k2 = 196 k = +√196 k = +14

  4. Solving Quadratic Equations Solve the equation by using square roots. r2 + 49 = 49 r = 0 w2 – 36 = -64 w2 = -28 w = +√-28 No solution 4g2 = 25 g2 = 25 4 g = +5 2

  5. Solving Quadratic Equations Solve the equation by using square roots. 3a2 + 12 = 0 3a2 = -12 a2 = -4 a = +√-4 No solution

  6. Solving Quadratics by Square Roots Solve the equation by using square roots. (x – 5)2 = 64 x – 5 = +√64 x – 5 = +8 x = 5 + 8 OR x = 5 – 8 x = 13 OR x = -3 (6x + 3)2 = 121 6x + 3 = +√121 6x + 3 = +11 6x = -3 + 11 OR 6x = -3 – 11 6x = 8 OR 6x = -14 x = 4 OR x = -7 3 3

  7. Solving Quadratics Solve the equation by using square roots. (x – 4)2 + 5 = 69 (x – 4)2 = 64 x – 4 = +√64 x = 4 + 8 or x = 4 – 8 x = 12 or -4 (x – 3)2 = ¼ x – 3 = +½ x = 3 + ½ x = 7 or -5 2 2

  8. Solving Quadratics Solve the equation by using square roots. (x – 4)2 = 7 x – 4 = +√7 x = 4 + √7 *Leave your answers with the square root sign if you are not told what to round to!

  9. Solving Real World Quadratics by Square Roots A museum is planning an exhibit that will contain a large globe. The surface area of the globe will be 315ft2. Find the radius, to the nearest whole number, of the sphere producing this surface area. Use the equation S = 4Πr2, where S is the surface area and r is the radius. S = 4Πr2 315 = 4Πr2 315 = r2 4Π r ≈ 5 *length is positive so we disregard the negative root.

  10. Solving Real World Quadratics by Square Roots A city is planning a circular duck pond for a new park. The depth of the pond will be 4ft. Because of water resources, the maximum volume will be 20,000ft3. Find the radius of the pond to the nearest tenth. Use the equation V = Πr2h, where V is the volume, r is the radius, and h is the depth. r = 39.9

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