Please help me with the worksheet

Answer:

9)    a = ¾, vertex: (-4, 2),  Equation: y = ¾|x + 4| + 2

10)  a = ¼, vertex: (0, -3),  Equation: y = ¼|x - 0| - 3

11)   a = -4,  vertex: (3,  1),   Equation: y = -4|x - 3| + 1

12)  a = 1,    vertex: (-2, -2),  Equation: y = |x + 2| - 2

Step-by-step explanation:

I could only work on questions 9, 10, 11, 12 in accordance with Brainly's rules. Nevertheless, the techniques demonstrated in this post applies to all of the given problems in your worksheet.

The given set of graphs are examples of absolute value functions. The general form of absolute value functions is: y = a|x – h| + k, where:

|a|  = determines the vertical stretch or compression factor (wideness or narrowness of the graph).

(h, k) = vertex of the function

x = h represents the axis of symmetry.

Solve for a:

In order to solve for the value of a, choose another point on the graph, (0, 5) and substitute into the general form (equation):

y = a|x – h| + k

5 = a| 0 - (-4)| + 2

5 = a| 0 + 4 | + 2

5 = a|4| + 2

5 = 4a + 2

Subtract 2 from both sides:

5 - 2 = 4a + 2 - 2

3 = 4a

Divide both sides by 4 to solve for a:

[tex]\LARGE\mathsf{\frac{3}{4}\:=\:\frac{4a}{4}}[/tex]

a = ¾

Therefore, given the value of a = ¾, and the vertex, (-4, 2), then the equation of the absolute value function is:

Equation:  y = ¾|x + 4| + 2

Solve for a:

In order to solve for the value of a, choose another point on the graph, (4, -2) and substitute into the general form (equation):

y = a|x – h| + k

-2 = a|4 - 0| -3

-2 = a|4| - 3

-2 = 4a - 3

Add 3 to both sides:

-2 + 3 = 4a - 3 + 3

1 = 4a  

Divide both sides by 4 to solve for a:

[tex]\LARGE\mathsf{\frac{1}{4}\:=\:\frac{4a}{4}}[/tex]

a = ¼

Therefore, given the value of a = ¼, and the vertex, (0, -3), then the equation of the absolute value function is:

Equation:  y = ¼|x - 0| - 3

Solve for a:

In order to solve for the value of a, choose another point on the graph, (4, -3) and substitute into the general form (equation):

y = a|x – h| + k

-3 = a|4 - 3| + 1

-3 = a|1| + 1

-3 = a + 1

Subtract 1 from both sides to isolate a:

-3 - 1 = a + 1 - 1

a = -4

Therefore, given the value of a = -4, and the vertex, (3, 1), then the equation of the absolute value function is:

Equation:  y = -4|x - 3| + 1

Solve for a:

In order to solve for the value of a, choose another point on the graph, (-4, 0) and substitute into the general form (equation):

y = a|x – h| + k

0 = a|-4 - (-2)| - 2

0 = a|-4 + 2| - 2

0 = a|-2| - 2

0 = 2a - 2

Add 2 to both sides:

0 + 2  = 2a - 2 + 2

2 = 2a

Divide both sides by 2 to solve for a:

[tex]\LARGE\mathsf{\frac{2}{2}\:=\:\frac{2a}{2}}[/tex]

a = 1

Therefore, given the value of a = -1, and the vertex, (-2, -2), then the equation of the absolute value function is:

Equation:  y = |x + 2| - 2

Select all the statements that are true for △ABC.A. AH is an altitude.
B. IH is a median.
C. JC is a median.
D. The medians and altitudes intersect at the same point.
E. The altitudes intersect outside of the triangle.

(a) A box contains 7 red balls, 6 white balls, and 7 black balls. Two balls are drawn at random from the box (with replacement of the first before the second is drawn). What is the probability of getting a red ball on the first draw and a white ball on the second

PLZ HELP ASAP! WILL MARK BRAINLY

Mr. Reyes baked 4 batches of muffins for his class each batch had 12 muffins. if Mr. Reyes Has 24 students, How many muffins will each student receive?

Donny jumped from a rock into a lake. The rock is 35 feet above water. He dove 15 feet below the surface of the water. His brother says he traveled 20 feet in all. Donny says he traveled 50 feet in all. Who correct?

.
Solve using traditional division: 3,385 31.
109 R6
1009
108 R 37
109

Find the square root of the following: 36
121​

The price was reduced from two thousand, four hundred ninety-eight dollars to one thousand, nine hundred ninety- nine dollars. By how much was the price reduced?​

(REAL ANSWERS PLEASE)


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4
-2
2
-1
0
o
-2
1
-4
2
Without graphing, what is the y-intercept of this function?
es )
A)
(0,0)
B)
(-2, 1)
(2, -1)
D
(4, -2)

54,392 rounded to the hundreds place

Subtract from (4x- 5y+3z) from the sum of (9x+2y-3z), (-10x+ y- z) and (2x+ 3y+ 7z).
Explain​

1, 7, 13, 19, 25
Find the 20th linear term

6,600,000,000 exponential notation

HELPPPPPPPPPPPPPPPPPPP

There are 900 3-digit integers, the integers between 100 and 999, inclusive. What percent of these integers contain only odd digits

The sum of 13 and 3 times a number is 31. What is the number?

8488.75 times 24.50 plz quick

If the Owen family has a child in two years, how much can they expect to spend, per year, to raise the child from its birth to when it is five years old?

A) y = 5x

B) y = 10x

C) y = 7.5x

D) y = 30x​

3. How many 1/8's are in 1 1/4?

Simplify the ratio 25 :15

15.
The number of calories in a 100-g serving of fruit varies by the type of fruit. A snack consisting of
on serving each of peach, apple, and banana contains 124 calories. A snack consisting of two
servings of peach and one serving of banana contains 160 calories. A snack consisting of one
serving of peach, 2 servings of apple, and two servings of banana contains 188 calories. How
many calories are in a 100-g serving of each type of fruit?

· Carlos ran one lap in 1 minute 3 seconds. Orlando rana one lap 5 seconds faster than Carlos. How many seconds did it take Orlando to run one lap?​

33% of what number is 1.45? Round to the nearest tenth.

Bạn dự định đi học thêm vào mùa hè này. Nếu đi học bạn sẽ không thể đi làm với thu nhập là 5 triệu đồng và không thể ở nhà nghỉ ngơi. Học phí là 2 triệu, tiền mua giáo trình 300 ngàn, sinh hoạt phí là 1.5 triệu. Hãy xác định chi phí cơ hội của việc đi học thêm vào mùa hè này.

please help, im literally so tired

A type of bacterium triples in population every hour. Assuming you start with
80 bacteria, the formula that models the number of bacteria at the beginning
of hour nis:
a(n) = 80 • 31-1
How many bacteria will there be at the beginning of hour 5?
A. 19,440
B. 1200
C. 720
D. 6480

8 glasses every 24 hours

Plx = 3 + 5x+2
Degree
Leading coefficient
Turning Points
End
Behavior of the
Graph

ILL GIVE BRAINLIEST! THIS IS DUE SOON PLEASE