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1) Sea la función $f(x)=x^2+5x+1$. Determine el valor de $f(3)$.

A) $15$

B) $22$

C) $25$

D) $29$

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Debemos reemplazar en la función $f(x)=x^2+5x+1$, el valor de $x$ por $3$, obteniendo:

$f($[[0]]$)=($[[0]]$)^2+5 \\cdot$ [[0]] $+1$

$f($[[0]]$)=$[[1]]$+$[[2]]$+1$

$f($[[0]]$)=$[[3]]

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La respuesta es: [[0]]

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3) ¿Cuáles son las coordenadas del punto de corte en el eje Y de la función $f(x)=4x^2+5x-9$?

A) $(0,-9)$

B) $(0,9)$

C) $(0,4)$

D) $(0,-4)$

Para determinar las coordenadas de corte del eje Y con la función cuadrática $f(x)=ax^2+bx+c$, debemos seguir los siguientes pasos:

Paso 1: Determinar el valor de $c$ en la función $f(x)=4x^2+5x-9$, el cual es [[0]].

Paso 2: Determinar la coordenada de corte del eje Y, usando la fórmula $(0,c)=($[[1]]$,$[[2]]$)$

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La respuesta es: [[0]]

2) Determine la ecuación del eje de simetría de la parábola de la función $f(x)=2x^2-8x+12$.

A) $x=-2$

B) $x=-3$

C) $x=2$

D) $x=3$

Para determinar el eje de simetría de uan función cuadrática de la forma $f(x)=ax^2+bx+c$, debemos seguir los siguientes pasos:

Paso 1: Determinar los valores de $a$ y $b$ en la función $f(x)=2x^2-8x+12$ (no olvides incluir sus signos)

$a=$[[0]]

$b=$[[1]]

Paso 2: Usar la fórmula del eje de simetría $x=$ $\\Large -\\frac{b}{2a}$, y luego simplificar la fracción obtenida, en caso de ser posible.

[[1]] [[1]]

$x=$ $-$ _________ $=-$ _________ $=$ [[3]]

$2 \\cdot$ [[0]] [[2]]

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La respuesta es: [[0]]

4) ¿Cuáles son las coordenadas del vértice de la parábola cuya función es $f(x)=x^2+6x+2$?

A) $(7,3)$

B) $(-7,-3)$

C) $(-3,7)$

D) $(-3,-7)$

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Para determinar el vértice de una parábola de la forma $f(x)=ax^2+bx+c$, debemos seguir los siguientes pasos:

Paso 1: Debemos usar la fórmula $x=$ $\\Large -\\frac{b}{2a}$, recordando que la función es $f(x)=x^2+6x+2$, por tanto, obtenemos que los valores de $a=$[[0]] y $b=$[[1]].

Paso 2: Reemplazar $a=$[[0]] y $b=$[[1]] en la fórmula:

[[3]] [[3]]

$x=$ $\\Large -\\frac{b}{2a}$$=-$ ____________$=-$________$=$[[5]]

$2 \\cdot$ [[2]] [[4]]

Paso 3: Reemplazamos el valor de la coordenada $x$ del paso 2, el cual es [[0]] en la función $f(x)=x^2+6x+2$, obteniendo que la coordenada y es igual a:

$y=f($[[0]]$)=($[[0]]$)^2+6 \\cdot$ [[0]] $+2$

$y=f($[[0]]$)=$[[1]][[2]]$+2$

$y=f($[[0]]$)=$[[3]]

Paso 4: Determinar la coordenada del vértice que es igual a $(x,y)=( $[[4]]$,$[[5]]$)$

La respuesta es: [[0]]

5) Determine las coordenadas de los puntos de corte del eje X de la función $f(x)=x^2+7x+12$.

A) $(-4,0)$ y $(3,0)$

B) $(4,0)$ y $(3,0)$

C) $(-4,0)$ y $(-3,0)$

D) $(4,0)$ y $(-3,0)$

Para determinar los puntos de corte en el eje X debemos resolver la ecuación de segundo grado $f(x)=x^2+7x+12=0$, para ello realizaremos los siguientes pasos:

Paso 1: En la ecuación $f(x)=x^2+7x+12=0$, debemos primero pensar en dos números $a$ y $b$ que cumplan las siguientes condiciones, que multiplicados sean igual a 12 y sumados sean igual a 7, estos dos números son $a=$[[0]] y $b=$[[1]]. (Observación aquí $a>b$)

Paso 2: Con los valores $a=$[[0]] y $b=$[[1]], obtenemos la siguiente factorización:

$(x+a) \\cdot (x+b)=0$=$(x+$[[2]]$)\\cdot(x+$[[3]]$)=0$

Paso 3: Determinamos de la factorización las ecuaciones:

$x+a=0$ y $x+b=0$

$x+$[[4]]$=0$ y $x+$[[5]]$=0$

Paso 4: Despejamos las ecuaciones del paso 3, obteniendo que las coodenadas x de los puntos de corte del eje X son:

$x_1=$[[6]] y $x_2=$[[7]]

Paso 5: Las coordenadas de corte son $(x_1,0)=($[[8]] $,0)$ y $(x_2,0)=($[[9]] $,0)$

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La respuesta es: [[0]]

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