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What is the equation of the quadratic function with a vertex at (2,-25) and an x-intercept at (7,0)?

skelet666 [1.2K]

Answer: f(x) = (x + 3)(x – 7)

Step-by-step explanation: Use "standard form" of the function and insert values given: vertex (2,-25) intercept point (7,0)

f(x) = a(x-h)² + k from vertex, h is 2 y is -25 from intercept, x is 7 f(x) is 0

to find a, 0 = a(7-2)² +(-25) 0 = a(7-2)² -25 add 25 to both sides

25 = a(5)² 25 = 25a 25/25 = a 1=a (seems useless but verifies implied "a"coefficient is 1)

f(x) = a(x-h)² + k solve to get the quadratic form

f(x) = (x-2)² -25 (x - 2)² is x² -4x +4

f(x) = x² -4x +4 -25 simplify

f(x) = x² -4x - 21 then factor

f(x) = (x + 3)(x - 7)

8 0

2 years ago

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equatio

Mama L [17]

We can tell from the data that there is a midpoint between the lowest and highest point of the clock, which is at a height of 9.5 feet.
Moreover, the lowest point occurs at 6 o clock, and the highest occurs at 12 o clock.
The amplitude of variation from the mid-point is 0.5 feet given by (10 - 9) / 2.
Finally, the time period for the equation is 12 hours. Thus, the answer is:
h = 0.5cos(πt/6) + 9.5, option B

5 0

2 years ago

i will mark as brainiest Jared is using a 100 ft rope to set up a kite-shaped area for food vendors. He has started roping off t

blsea [12.9K]

Sample Response: A kite has two pairs of congruent adjacent sides and opposite sides that are not congruent. Jared has already created one pair of congruent adjacent sides. Since he has used 60 ft of rope, there are 40 ft remaining. This means that he will need 20 ft of rope for each of the other sides, or half of the remaining rope, in order to create another pair of congruent adjacent sides. Since this is a different length than 30 ft, the shape has opposite sides that are not congruent.

4 0

2 years ago

Read 2 more answers

Jenny is eight years older then twice her cousin sues age. The sum of their ages is less then 32. What is the greatest age that

maw [93]

Answer:

The age of Sue could be 7 years

Step-by-step explanation:

Jenny is 8 years older than twice her cousin Sue's age.

The first equation will be :

J = 8 + 2S ---------(1)

The sum of their ages is less than 32.

The second equation will be :

J + S < 32 ----------------(2)

Now rearrange both equations :

8 + 2S + S < 32

3S < 32 - 8

3S < 24

S < 24/3

S < 8

S = 7

The age of Sue could be 7 years.

3 0

1 year ago

370 College freshmen were interviewed. 200 were registered for an Advanced Math class. 270 were registered for an English class

frozen [14]

Answer:

Step-by-step explanation:

To aid in understanding, draw three circles...

100 were registered for both Math and English.

50 were registered for both Sport and English but not Math.

70 were registered for Math, Sport, and English.

From here we will be able to calculate for those that signed up for only English class: Total number of students that signed up for english class

a. none signed up only for Maths (refer to attached document)

b. How many signed up for neither Math nor English meaning they signed up for only sports which is 70 from the venn diagram in the attachment.

c. How many signed up for an English class and at least one other class?

From the venn diagram:

we could have an English class and maths class - 100

we could also have an a English class and sports - 50

Thus total is 150.

d. What is the total fee for all the students enrolled in classes

From the diagram, 120 (english only and sport only) enrolled for only one class = 120 x $100 = $12,000

From the diagram, 180 (english and sport, maths and sport and english and maths) enrolled for two classes = 180 x $150 = $27,000

From the diagram, only 70 enrolled for the three classes = 70 x $200 = $14,000

Total fees = $12,000 + $27,000 + $14,000 = $53,000

5 0

2 years ago

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