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9.9E: Ejercicios

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La práctica hace la perfección

Ejercicio$$\PageIndex{11}$$ Solve Quadratic Inequalities Graphically

En los siguientes ejercicios,

1. Resolver gráficamente
2. Escribir la solución en notación de intervalos
1. $$x^{2}+6 x+5>0$$
2. $$x^{2}+4 x-12<0$$
3. $$x^{2}+4 x+3 \leq 0$$
4. $$x^{2}-6 x+8 \geq 0$$
5. $$-x^{2}-3 x+18 \leq 0$$
6. $$-x^{2}+2 x+24<0$$
7. $$-x^{2}+x+12 \geq 0$$
8. $$-x^{2}+2 x+15>0$$
Contestar

1.

1. Figura 9.8.16
2. $$(-\infty,-5) \cup(-1, \infty)$$

3.

1. Figura 9.8.17
2. $$[-3,-1]$$

5.

1. Figura 9.8.18
2. $$(-\infty,-6] \cup[3, \infty)$$

7.

1. Figura 9.8.19
2. $$[-3,4]$$
Ejercicio$$\PageIndex{12}$$ Solve Quadratic Inequalities Graphically

En los siguientes ejercicios, resolver cada desigualdad algebraicamente y escribir cualquier solución en notación de intervalos.

1. $$x^{2}+3 x-4 \geq 0$$
2. $$x^{2}+x-6 \leq 0$$
3. $$x^{2}-7 x+10<0$$
4. $$x^{2}-4 x+3>0$$
5. $$x^{2}+8 x>-15$$
6. $$x^{2}+8 x<-12$$
7. $$x^{2}-4 x+2 \leq 0$$
8. $$-x^{2}+8 x-11<0$$
9. $$x^{2}-10 x>-19$$
10. $$x^{2}+6 x<-3$$
11. $$-6 x^{2}+19 x-10 \geq 0$$
12. $$-3 x^{2}-4 x+4 \leq 0$$
13. $$-2 x^{2}+7 x+4 \geq 0$$
14. $$2 x^{2}+5 x-12>0$$
15. $$x^{2}+3 x+5>0$$
16. $$x^{2}-3 x+6 \leq 0$$
17. $$-x^{2}+x-7>0$$
18. $$-x^{2}-4 x-5<0$$
19. $$-2 x^{2}+8 x-10<0$$
20. $$-x^{2}+2 x-7 \geq 0$$
Contestar

1. $$(-\infty,-4] \cup[1, \infty)$$

3. $$(2,5)$$

5. $$(-\infty,-5) \cup(-3, \infty)$$

7. $$[2-\sqrt{2}, 2+\sqrt{2}]$$

9. $$(-\infty, 5-\sqrt{6}) \cup(5+\sqrt{6}, \infty)$$

11. $$\left(-\infty,-\frac{5}{2}\right] \cup\left[-\frac{2}{3}, \infty\right)$$

13. $$\left[-\frac{1}{2}, 4\right]$$

15. $$(-\infty, \infty)$$

17. sin solución

19. $$(-\infty, \infty)$$

Ejercicio$$\PageIndex{13}$$ Writing Exercises
1. Explicar los puntos críticos y cómo se utilizan para resolver las desigualdades cuadráticas algebraicamente.
2. Resuelve$$x^{2}+2x≥8$$ tanto gráfica como algebraicamente. ¿Qué método prefieres y por qué?
Contestar

1. Las respuestas pueden variar.

3. Las respuestas pueden variar.

Autocomprobación

a. después de completar los ejercicios, utilice esta lista de verificación para evaluar su dominio de los objetivos de esta sección.

b. En una escala del 1 al 10, ¿cómo calificaría su dominio de esta sección a la luz de sus respuestas en la lista de verificación? ¿Cómo se puede mejorar esto?

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