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3 years ago

Consider the function f(x) = 3x2 + 7x + 2.

2 answers:

5 0

The discriminant:
D = b² - 4 a c = 7² - 4· 3 · 2 = 49 - 24 = 25
D > 0 This function has 2 x-intercepts ( 2 zeroes ).
x 1 = (-7+5)/6 =-1/3
x 2 = (-7-5) / 6 = - 2

STatiana [176]3 years ago

4 0

Answer:

25,2 & two real number solutions

Step-by-step explanation:

Edge 2020

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Answer:

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Step-by-step explanation:

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3 years ago

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4 years ago

Plot point C(2,7). If M is the midpoint of CD , what are the coordinates of D?

Y_Kistochka [10]

Answer:

The coordinates of D is (-4,-9)

Step-by-step explanation:

Given

C = (2,7)

M=(-1,-1) ----- Missing part of question

Required

Determine the coordinates of D

Let the coordinates of D be (x₂,y₂)

We'll solve this question using mid point formula;

$M(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Where

$C(x_1,y_1) = (2,7)$ and $M(x,y) = (-1,-1)$

Put these values in the formula

$(-1,-1) = (\frac{2+x_2}{2},\frac{7+y_2}{2})$

By comparison;

$-1 = \frac{2+x_2}{2}$ and $-1 = \frac{7+y_2}{2}$

$-1 = \frac{2+x_2}{2}$

Multiply both sides by 2

$-2 = 2 + x_2$

Subtract 2 from both sides

$-2 -2 = x_2$

$x_2 = -4$

$-1 = \frac{7+y_2}{2}$

Multiply both sides by 2

$-2 = 7 + y_2$

Subtract 7 from both sides

$-2 - 7 = y_2$

$y_2 = -9$

Hence, the coordinates of D is (-4,-9)

4 0

4 years ago

Halla la tasa de variación de cada funcion en el intervalo [-4,3] e indica si es positiva , negativa o nula A) f(x)=x2-2x+4 B) f

masya89 [10]

Answer:

$A) \hspace{3}Rate\hspace{3}of\hspace{3}change=-5\hspace{3}Negative\\\\B)\hspace{3}Rate\hspace{3}of\hspace{3}change=-21\hspace{3}Negative$

Step-by-step explanation:

Given a function $f(x)$ , we called the rate of change to the number that represents the increase or decrease that the function experiences when increasing the independent variable from one value " $x_1$ " to another " $x_2$ ".

The rate of change of $f(x)$ between $x_1$ and $x_2$ can be calculated as follows:

$Rate\hspace{3}of\hspace{3}change=f(x_2)-f(x_1)$

For:

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

Let's find $f(x_1)$ and $f(x_2)$ , where:

$[x_1,x_2]=[-4,3]$

$f(x_1)=f(-4)=(-4)^2-2(4)+4=16-8+4=12\\f(x_2)=f(3)=(3)^2-2(3)+4=9-6+4=7$

So:

$Rate\hspace{3}of\hspace{3}change =7-12=-5\hspace{3}Negative$

And for:

$f(x)-3x+2$

Let's find $f(x_1)$ and $f(x_2)$ , where:

$[x_1,x_2]=[-4,3]$

$f(x_1)=f(-4)=-3(-4)+2=12+2=14\\f(x_2)=f(3)=-3(3)+2=-9+2=-7$

So:

$Rate\hspace{3}of\hspace{3}change =-7-14=-21\hspace{3}Negative$

Translation:

Dada una función $f(x)$ , llamábamos tasa de variación al número que representa el aumento o disminución que experimenta la función al aumentar la variable independiente de un valor " $x_1$ " a otro " $x_2$ ".

La tasa de variación de $f(x)$ entre $x_1$ y $x_2$ , puede ser calculada de la siguiente forma:

$Tasa\hspace{3}de\hspace{3}variacion=f(x_2)-f(x_1)$

Para:

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

Encontremos $f(x_1)$ y $f(x_2)$ , donde:

$[x_1,x_2]=[-4,3]$

$f(x_1)=f(-4)=-3(-4)+2=12+2=14\\f(x_2)=f(3)=-3(3)+2=-9+2=-7$

Entonces:

$Tasa\hspace{3}de\hspace{3}variacion =7-12=-5\hspace{3}Negativa$

Y para:

$f(x)-3x+2$

Encontremos $f(x_1)$ y $f(x_2)$ , donde:

$[x_1,x_2]=[-4,3]$

$f(x_1)=f(-4)=-3(-4)+2=12+2=14\\f(x_2)=f(3)=-3(3)+2=-9+2=-7$

Entonces:

$Tasa\hspace{3}de\hspace{3}variacion=-7-14=-21\hspace{3}Negativa$

8 0

4 years ago