Name a pair of adjacent angles

Which equation represents a graph with a vertex at (–3, 2)?

lesya [120]

We will proceed to find the equations in the vertex form in each case

Part a) $y= 4x^{2}+24x+38$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$y-38= 4x^{2}+24x$

Factor the leading coefficient

$y-38= 4(x^{2}+6x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$y-38+36= 4(x^{2}+6x+9)$

$y-2= 4(x+3)^{2}$

$y= 4(x+3)^{2}+2$

the vertex is the point $(-3,2)$

Part b) $y=4x^{2}-24x+38$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$y-38= 4x^{2}-24x$

Factor the leading coefficient

$y-38= 4(x^{2}-6x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$y-38+36= 4(x^{2}-6x+9)$

$y-2= 4(x-3)^{2}$

$y= 4(x-3)^{2}+2$

the vertex is the point $(3,2)$

Part c)  $y=4x^{2}+12x+2$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$y-2= 4x^{2}+12x$

Factor the leading coefficient

$y-2= 4(x^{2}+3x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$y-2+9= 4(x^{2}+3x+2.25)$

$y+7= 4(x+1.5)^{2}$

$y= 4(x+1.5)^{2}-7$

the vertex is the point $(-1.5,7)$

Part d) $y=4x^{2}+16x+13$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$y-13= 4x^{2}+16x$

Factor the leading coefficient

$y-13= 4(x^{2}+4x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$y-13+16= 4(x^{2}+4x+4)$

$y+3= 4(x+2)^{2}$

$y= 4(x+2)^{2}-3$

the vertex is the point $(-2,-3)$

therefore

the answer is

$y= 4x^{2}+24x+38$

3 0

3 years ago

Read 2 more answers

216+5( 8+1/5) Please i need it asap ty!

AysviL [449]

216+5X41/5
216+41
257
Please brainlyest

6 0

3 years ago

Read 2 more answers

Find the missing length

Lesechka [4]

Answer:

the answer is 46

Step-by-step explanation:

8 + 20 + 18 = 46

i hope this helps

8 0

3 years ago

Read 2 more answers

Which expression is an irrational number? A. 20 B.(10^2) C.144 D.0.48

tankabanditka [31]

Hello from MrBillDoesMath!

Answer: All numbers provided are rational

Discussion:

20 = 20/1 => rational

10^2 = 100 => rational

144 = 144/1 => rational

0.48 = 48/100 => rational

Thank you,

MrB

7 0

4 years ago

Which table represents an arithmethic sequence?

Fiesta28 [93]

Table 3 represents an arithmetic sequence.

Solution:

To find which table represents an arithmetic sequence:

In arithmetic sequence difference of each term is equal.

$d=a_n-a_{n-1}$

Table 1:

$d=a_2-a_1$

= –12 – (–6)

d = –6

$d=a_3-a_2$

= –24 – (–12)

d = –12

Here differences are not equal.

So table 1 not represents an arithmetic sequence.

Table 2:

$d=a_2-a_1$

= 9 – 7

d = 2

$d=a_3-a_2$

= 13 – 9

d = 4

Here differences are not equal.

So table 2 not represents an arithmetic sequence.

Table 3:

$d=a_2-a_1$

= 7.3 – 8.7

d = –1.4

$d=a_3-a_2$

= 5.9 – 7.3

d = –1.4

$d=a_4-a_3$

= 4.5 – 5.9

d = –1.4

$d=a_5-a_4$

= 3.1 – 4.5

d = –1.4

Here differences are equal.

So table 3 represents an arithmetic sequence.

8 0

3 years ago