Guía de ejercicios Función Cuadrática 2° medio

Guía de ejercicios Función Cuadrática. ====================================== Nombre:\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ Curso:\_\_\_\_\_\_\_ -------------------------------------------------------------------------...

Guía de ejercicios Función Cuadrática. ====================================== Nombre:\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ Curso:\_\_\_\_\_\_\_ ------------------------------------------------------------------------------------------------------------- Instrucciones: Lee atentamente las instrucciones de cada Ítem y registre su desarrollo, en el espacio dado. ------------------------------------------------------------------------------------------------------------- +-----------------------------------------------------------------------+ | Ítem 1: Determina el tipo de concavidad, vértice, eje de simetría e | | intersección con los ejes de la siguiente función. Luego, esboza su | | gráfico y determina Dominio y Recorrido. | | | | +--------------------------------+--------------------------------+ | | | Función: | \ | | | | | [*f*(*x*) = *x*^2^ + 2*x* + 1] | | | | | {.math | | | | |.display}\ | | | +================================+================================+ | | | Concavidad: | | | | +--------------------------------+--------------------------------+ | | | Vértice: | | | | +--------------------------------+--------------------------------+ | | | Eje de Simetría: | | | | +--------------------------------+--------------------------------+ | | | Intersección con sus ejes: | | | | +--------------------------------+--------------------------------+ | | | Dominio y Recorrido: | \ | | | | | [*Dom* *f*:]{.math.display}\ | | | | | | | | | | \ | | | | | [*Rec* *f*:]{.math.display}\ | | | +--------------------------------+--------------------------------+ | | | Grafico: | | | | +--------------------------------+--------------------------------+ | | | | +--------------------------------+--------------------------------+ | | | Función: | \ | | | | | [*f*(*x*) =  − *x*^2^ − 4*x* − | | | | |  3]{.math | | | | |.display}\ | | | +================================+================================+ | | | Concavidad: | | | | +--------------------------------+--------------------------------+ | | | Vértice: | | | | +--------------------------------+--------------------------------+ | | | Eje de Simetría: | | | | +--------------------------------+--------------------------------+ | | | Intersección con sus ejes: | | | | +--------------------------------+--------------------------------+ | | | Dominio y Recorrido: | \ | | | | | [*Dom* *f*:]{.math.display}\ | | | | | | | | | | \ | | | | | [*Rec* *f*:]{.math.display}\ | | | +--------------------------------+--------------------------------+ | | | Grafico: | | | | +--------------------------------+--------------------------------+ | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | Ítem 2: Determine el vértice de las siguientes funciones cuadráticas: | | | | +------------------------------------------------------------------+ | | | \ | | | | [*f*(*x*) = *x*^2^ − 2*x* − 15]{.math.display}\ | | | | | | | | Vértice: | | | | | | | | \ | | | | [*Dom* *f*(*x*):*Rec* *f*(*x*):]{.math.display}\ | | | +==================================================================+ | | | \ | | | | [*g*(*x*) =  − 3*x*^2^ − 6*x* + 2]{.math.display}\ | | | | | | | | Vértice: | | | | | | | | \ | | | | [Dom *g*(*x*):Rec *g*(*x*):]{.math.display}\ | | | +------------------------------------------------------------------+ | | | \ | | | | [*h*(*x*) = 2*x*^2^ − 20*x* + 5]{.math.display}\ | | | | | | | | Vértice: | | | | | | | | \ | | | | [Dom *h*(*x*):]{.math.display}\ | | | +------------------------------------------------------------------+ | | | \ | | | | [*i*(*x*) =  − *x*^2^ − 2*x* + 1]{.math.display}\ | | | | | | | | Vértice: | | | | | | | | \ | | | | [Dom *i*(*x*):Rec *i*(*x*):]{.math.display}\ | | | +------------------------------------------------------------------+ | | | \ | | | | [*j*(*x*) = *x*^2^ + 8*x* + 16]{.math.display}\ | | | | | | | | Vértice: | | | | | | | | \ | | | | [Dom *j*(*x*):Rec *j*(*x*):]{.math.display}\ | | | +------------------------------------------------------------------+ | +-----------------------------------------------------------------------+ +-----------------------------------------------------------------------+ | Ítem 3: Lee atentamente y encierra la alternativa correcta: | | | | +------------------------------------------------------------------+ | | | 6. ¿Cuál de las siguientes funciones corresponde a una función | | | | cuadrática? | | | | | | | | | | | | | | | | a. [*f*(*x*) = 3^2^*x* + 1]{.math.inline} | | | | | | | | b. [*h*(*x*) = *x*^2^ + 8]{.math.inline} | | | | | | | | c. [\$p\\left( x \\right) = \\sqrt{x\^{2} + 3x - 1}\\ \$]{.math | | | |.inline} | | | | | | | | d. [\$f\\left( x \\right) = \\frac{1}{x\^{2}}\$]{.math.inline} | | | | | +==================================================================+ | | | 1. Las raíces (o soluciones) de la ecuación | | | | [*x*^2^ + 13*x* − 30 = 0]{.math.inline} son: | | | | | | | | | | | | | | | | a. {.math.inline} y [ − 2]{.math.inline} | | | | | | | | b. [10 ]{.math.inline}y [ − 3]{.math.inline} | | | | | | | | c. [5 ]{.math.inline}y [ − 6]{.math.inline} | | | | | | | | d. {.math.inline} y [ − 15]{.math.inline} | | | +------------------------------------------------------------------+ | | | 2. Las raíces (o soluciones) de la ecuación | | | | [*x*(*x*−1) = 42]{.math.inline} son: | | | | | | | | | | | | | | | | a. [\$\\sqrt{43}\$]{.math.inline} y [\$- \\sqrt{43}\$]{.math | | | |.inline} | | | | | | | | b. [7 ]{.math.inline}y {.math.inline} | | | | | | | | c. [7 ]{.math.inline}y [ − 6]{.math.inline} | | | | | | | | d. {.math.inline} y [ − 21]{.math.inline} | | | +------------------------------------------------------------------+ | | | 3. Si [*f*(*x*)= *x*^2^ − 5]{.math.inline}, su gráfico es: | | | +------------------------------------------------------------------+ | | | 4. El gráfico de la figura adjunta podría | | | | corresponder a la función cuadrática: | | | | | | | | | | | | | | | | a. [*f*(*x*) = 3 + 2*x* − *x*^2^]{.math.inline} | | | | | | | | b. [*f*(*x*) = *x*^2^ − 2*x* + 3]{.math.inline} | | | | | | | | c. [*f*(*x*) = *x*^2^ + 2*x* − 3]{.math.inline} | | | | | | | | d. [*f*(*x*) = *x*^2^ − 2*x*]{.math.inline} | | | +------------------------------------------------------------------+ | | | 5. El recorrido de la función | | | | [*f*(*x*) =  − 2*x*^2^ + 4*x* + 5]{.math.inline} es: | | | | | | | | | | | | | | | | a. [\] − ∞,  − 1\]]{.math.inline} | | | | | | | | b. [\] − ∞, 1\]]{.math.inline} | | | | | | | | c. [\] − ∞, 7\]]{.math.inline} | | | | | | | | d. [\[7,  + ∞\[]{.math.inline} | | | +------------------------------------------------------------------+ | +-----------------------------------------------------------------------+