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3 years ago

Identify the vertex and the axis of symmetry of the graph of the function y = 2(x+2)2 - 4

Mathematics

2 answers:

Mekhanik [1.2K]3 years ago

7 0

Answer:

Part 1) The vertex is the point $(-2,-4)$

Part 2) The axis of symmetry is equal to $x=-2$

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

$y=a(x-h)^{2}+k$

where

(h,k) is the vertex of the parabola

The axis of symmetry of a vertical parabola is equal to

$x=h$ ----> the x-coordinate of the vertex

In this problem we have

$y=2(x+2)^{2}-4$

The vertex is the point $(-2,-4)$

The axis of symmetry is equal to the coordinate of the vertex

$x=-2$

see the attached figure to better understand the problem

Rashid [163]3 years ago

3 0

(-2, -4) Would be your answer written in standard form.

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Un terreno ha sido cultivado con tres variedades de claveles. La sexta parte ha sido sembrada por

Minchanka [31]

Answer:

1) Se siembra cinco doceavas partes del terreno con claveles rojos y amarillos, 2) Se siembra siete doceavas partes del terreno con claveles blancos.

Step-by-step explanation:

El enunciado se encuentra incompleto. La pregunta faltante es:

2 ¿Qué parte del terreno corresponde a los claveles blancos?

1) Sea $A$ el área total sembrada con los tres tipos de claveles. Entonces, las áreas sembradas con claveles rojos y claveles amarillos son $\frac{1}{6}\cdot A$ y $\frac{1}{4} \cdot A$ , respectivamente.

El área sembrada con claveles rojos y amarillos se obtiene al sumar las áreas correspondientes, es decir:

$x = \frac{1}{6}\cdot A + \frac{1}{4}\cdot A$

$x = \left(\frac{1}{6}+\frac{1}{4}\right)\cdot A$

$x = \left(\frac{4+6}{24} \right)\cdot A$

$x = \frac{10}{24}\cdot A$

$x = \frac{5}{12}\cdot A$

Se siembra cinco doceavas partes del terreno con claveles rojos y amarillos.

2) El área sembrada con claveles blancos se obtiene al sustraer el área obtenida en el punto anterior del área total. Esto es:

$x = A - \frac{5}{12}\cdot A$

$x = \left(1-\frac{5}{12} \right)\cdot A$

$x = \left(\frac{12}{12}-\frac{5}{12} \right)\cdot A$

$x = \left(\frac{12-5}{12} \right)\cdot A$

$x = \frac{7}{12}\cdot A$

Se siembra siete doceavas partes del terreno con claveles blancos.

8 0

4 years ago

Volumes of the solids with disk or shell method?

lina2011 [118]

The answer to the questions of volumes are given as follows

a) $v=128 \pi$

b) $v=\frac{128}{3} \pi$

c) $v=\frac{1024}{5} \pi$

d) $V=\frac{13568}{15} \pi$

Generally, the questions are mathematically solved below

$y=\sqrt{x}, y=4, x=0$

a) x-axis

if $y=4, x=16, x=0$

Using disk method

$} v=\pi \int_{0}^{16}(\sqrt{x})^{2} d x \\$

$v=\pi\left(\frac{x^{2}}{2}\right)_{0}^{16} \\$

$v=\frac{\pi}{2} \times 16 \times 16 \\$

$v=128 \pi$

b) line y=4

if x=0, y=0 ;

$y=\sqrt{x} \Rightarrow x=y^{2}$

Using shell method

$v = \int_{0}^{4} 2 \pi(4-y) \cdot y^{2} d y \\$

$v=2 \pi \int_{0}^{4}\left(4 y^{2}-y^{3}\right) d y$

$v=2 \pi\left[\frac{4 y^{3}}{3}-\frac{y^{4}}{4}\right]_{0}^{4} \\$

$v=\frac{2 \pi}{12}[1024-768] \\$

$v=\frac{512 \pi}{12} \\$

$v=\frac{128}{3} \pi$

c) y-axis

0 ≤ y ≤ 4

x=y^2

Using disk method

volume

$v=\pi \int_{0}^{4} y^{4} d y$$

$v=\pi\left(\frac{y 5}{5}\right)_{0}^{4} \\$

$v=\frac{1024}{5} \pi$

d) line x=-1

y=√x, y=4, x=0

0 ≤ x ≤ 6

Using shell method

volume is

$V=\int_{0}^{16} 2 \pi(1+x) \sqrt{x} d x$$

$V=2 \pi\int_{0}^{16}(x^{1 / 2}+x^{3 / 2}\right) )d x\right. \\$

$V=2 \pi\left[\frac{x^{3 / 2}}{3 / 2}+\frac{x^{5 / 2}}{5 / 2}\right]_{0}^{16} \\$

$V=2 \pi\left[2 / 3 \cdot\left(4^{2}\right)^{3 / 2}+2 / 5\left(4^{2}\right)^{5 / 2}\right] \\$

$V=4 \pi / 3 \cdot 4^{3}+4 \pi / 5 \cdot 4^{5} \\$

$V=4 \pi\left(\frac{1}{3}+\frac{4^{2}}{5}\right)$

$V=\frac{256}{15}(5+48) \pi \\$

$V=\frac{256 \times 53}{15} \pi \\$

$V=\frac{13568}{15} \pi$

Read more about volumes

brainly.com/question/1578538

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8 0

2 years ago

Julie spent 2/3 of an hour running and 5/6 of an hour swimming. How much longer did she swim than run?

aniked [119]

Running = 2/3

Swimming = 5/6

5/6 - 2/3 = 5/6 - 4/6 = 1/6

Answer : She spent 1/6 hour longer swimming than running.

4 0

3 years ago

Read 2 more answers

Pls help give u brainlist

Elenna [48]

Answer:

The rate of change is $\frac{7}{4}$ or 1.75. That shows that the cost per video game is $1.75

Step-by-step explanation:

The change in y over change of x or slope can be calculated using the equation:

$m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }$ so take the last two points: (10, 25) and (15, 33.75).

33.75-25=8.75

15-10=5

8.75/5=1.75 (7/4)

x=video games

y=total cost

Since slope is change in y (cost) per change of x (video games), the answer is:

1.75 cost per video game

8 0

3 years ago

Point O is the incenter of ΔABC.

Oksi-84 [34.3K]

Answer:

QBO=12 degrees

Step-by-step explanation:

angle QAO=angle OAS so:

2x+6=4x-12

reducing:

2x=18

x=9

substituting x into QBO=3x-15 then:

angle QBO=3(9)-15=12 degrees

8 0

3 years ago

Read 2 more answers