11.7: Ecuaciones cuadráticas y aplicaciones- Respuestas a los ejercicios de tareas

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Propiedad Raíz Cuadrada

$7,-1$

$9, 5$

$4, -14$

$-9\pm\sqrt{37}$

$2\pm\sqrt{70}$

$-4\pm 3\sqrt{7}$

$\dfrac{2}{9},-\dfrac{4}{9}$

$\dfrac{11}{3},\dfrac{1}{3}$

$-6\pm 5\sqrt{3}$

$-\dfrac{1}{2}$

$4,-10$

$\pm 2\sqrt{2}$

$-9\pm 2\sqrt{7}$

$-8\pm 3\sqrt{5}$

$0,-3$

$-\dfrac{2}{7},-\dfrac{10}{7}$

$\dfrac{7}{4},\dfrac{3}{4}$

Completando la Plaza

$225$;$(x-15)^2$

$\dfrac{225}{4}$;$\left(x-\dfrac{15}{2}\right)^2$

$144$;$(a-12)^2$

$\dfrac{1}{324}$;$\left(r-\dfrac{1}{18}\right)^2$

$11,5$

$-1\pm i\sqrt{\dfrac{19}{2}}$

$-5+\sqrt{86}, -5-\sqrt{86}$

$-1\pm i\sqrt{21}$

$-5\pm 2i$

$1\pm i\sqrt{2}$

$4\pm i\sqrt{39}$

$-1\pm i\sqrt{\dfrac{43}{6}}$

$-\dfrac{5}{2}\pm\dfrac{i\sqrt{87}}{2}$

$\dfrac{7}{2}\pm\dfrac{i\sqrt{139}}{2}$

$\dfrac{9+\sqrt{21}}{2},\dfrac{9-\sqrt{21}}{2}$

$1,-\dfrac{5}{2}$

$4+2\sqrt{7},4-2\sqrt{7}$

$1\pm 2i\sqrt{\dfrac{11}{3}}$

$8+2\sqrt{29}, 8-2\sqrt{29}$

$1,-3$

$7+\sqrt{85},7-\sqrt{85}$

$x=1\pm 1\sqrt{\dfrac{21}{5}}$

$-1,-7$

$-2-i\sqrt{\dfrac{37}{3}}$

$\dfrac{-7+\sqrt{181}}{2},\dfrac{-7-\sqrt{181}}{2}$

$\dfrac{5}{2}\pm 3i\sqrt{7}$

$\dfrac{1}{2}\pm i\sqrt{163}$

$8,7$

Fórmula cuadrática

$\dfrac{\sqrt{6}}{2},-\dfrac{\sqrt{6}}{2}$

$\dfrac{\sqrt{6}}{2},-\dfrac{\sqrt{6}}{2}$

$3,-3$

$\dfrac{-3\pm i\sqrt{55}}{4}$

$\dfrac{-3+\sqrt{401}}{14},\dfrac{-3-\sqrt{401}}{14}$

$\dfrac{-1\pm i\sqrt{3}}{2}$

$\dfrac{7+3\sqrt{21}}{10},\dfrac{7-3\sqrt{21}}{10}$

$-1,-\dfrac{3}{2}$

$4,-9$

$\dfrac{-3+\sqrt{345}}{14},\dfrac{-3-\sqrt{345}}{14}$

$\pm\dfrac{i\sqrt{6}}{3}$

$\dfrac{-1\pm i\sqrt{29}}{5}$

$\pm\dfrac{i\sqrt{2}}{2}$

$\dfrac{3\pm i\sqrt{159}}{12}$

$\dfrac{-5+\sqrt{137}}{8},\dfrac{-5-\sqrt{137}}{8}$

$3,-\dfrac{1}{3}$

$\dfrac{-5+\sqrt{337}}{12},\dfrac{-5-\sqrt{337}}{12}$

$2\sqrt{2},-2\sqrt{2}$

$\dfrac{3\pm 3i\sqrt{5}}{7}$

$\dfrac{\sqrt{6}}{2},-\dfrac{\sqrt{6}}{2}$

Funciones cuadráticas de la gráfica

$clipboard_e3c2d0091b454c104a36fb2864601180f.png$
Figura 11.7.1

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Figura 11.7.2

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Figura 11.7.3

$clipboard_ef8fce125d4e416a83fd860b6e755c996.png$
Figura 11.7.4

$clipboard_ec5187c055aec40958b218b1e327d1348.png$
Figura 11.7.5

$clipboard_ee442b96e37414f705b0c1aac7b50f315.png$
Figura 11.7.6

$clipboard_e2155797705f3d7d845bab7cf1eb425ec.png$
Figura 11.7.7

$clipboard_e75d74f174ece55deb5e9ed72d659da8d.png$
Figura 11.7.8

$clipboard_e70a35b8e0f09014b7e380c36e51ea99e.png$
Figura 11.7.9

$clipboard_e4131ef3f97fb5fa6f1934b4cd61308ae.png$
Figura 11.7.10

$f(x)=3(x-1)^2$

$f(x)=\dfrac{1}{3}x^2$

$f(x)=4(x+4)^2$

$f(x)=3x^2-4$

$clipboard_ebb34a63aab3c87d3fd8f5ef4e7beae52.png$
Figura 11.7.11

$clipboard_e85eceb8974428bfcf0f2931e617dfcbd.png$
Figura 11.7.12

$clipboard_ef0d61b8e9541e8c755651df5d5bb05f3.png$
Figura 11.7.13

$clipboard_e8a753b3414427b7a120d47dbd2f7725e.png$
Figura 11.7.14

$clipboard_e35adafa0e55aa4aa7c9b7b7844b1801c.png$
Figura 11.7.15

Desigualdades cuadráticas

$(-\infty, 3)\cup (6,\infty )$
$[-4,6]$
$(-1,3)$
$(-\infty, -6]\cup [-4,\infty )$
$(-\infty ,2)\cup (2,\infty )$
$(-\infty, -4]\cup [2,\infty )$
$[1,3]$
$\left[-4,\dfrac{5}{3}\right]$
$(-\infty ,-4]\cup\left(\dfrac{5}{4},\infty\right)$
$\left(-1,\dfrac{1}{3}\right)$
$\left[0,\dfrac{7}{4}\right]$
$(-\infty, -6]\cup [0,\infty )$
Sin solución
Todos los números reales

Aplicaciones con funciones cuadráticas

$\left(\dfrac{5}{4},-\dfrac{57}{8}\right)$;$-\dfrac{57}{8}$
$\left(\dfrac{1}{2},-\dfrac{11}{2}\right)$;$-\dfrac{11}{2}$
$(-1,1)$;$1$
$27.65$;$3,896.99$
$19.39$;$2,236.84$
$22.76$;$2,666.19$
$25$;$8.88$
$45$;$14.88$
$11$;$551.25$ o$550$
$16$;$480.5$ o$480$
$10$;$361$ o$360$