1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Temka [501]
3 years ago
11

Diagram below shows the curve of a quadratic function

Mathematics
1 answer:
uranmaximum [27]3 years ago
3 0

Answer:

q = -8, k = 2.

r = -6.

Step-by-step explanation:

f(x) = (x - p)^2 + q

This is the vertex form of a quadratic where the vertex is at the point (p, q).

Now the x intercepts are at -6 and 2 and the curve is symmetrical about the line x = p.

The value of p is the midpoint of  -6 and 2 which is (-6+2) / 2 = -2.

So we have:

f(x) = 1/2(x - -2)^2 + q

f(x) = 1/2(x + 2)^2 + q

Now the graph passes through the point (2, 0) , where it intersects the x axis, therefore, substituting x = 2 and f(x) = 0:

0 = 1/2(2 + 2)^2 + q

0 = 1/2*16 + q

0 = 8 + q

q = -8.

Now convert this to standard form to find k:

f(x) = 1/2(x + 2)^2 - 8

f(x) = 1/2(x^2 + 4x + 4) - 8

f(x) = 1/2x^2 + 2x + 2 - 8

f(x) = 1/2x^2 + 2x - 6

So k = 2.

The  r  is the y coordinate when x = 0.

so r = 1/2(0+2)^2 - 8

=  -6.

You might be interested in
7a+5=61 what is a in the equation
MrRa [10]

Answer:

a=8

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
If f(x) =15x 2 + 10x, find f(-1)<br><br> Anyone know the answer?
Rom4ik [11]
I'm assuming the given function is f(x) = 15x^2 + 10x.

If so, then,

f(x) = 15x^2 + 10x
f(x) = 15*(x)^2 + 10*(x)
f(-1) = 15*(-1)^2 + 10*(-1) ... note how x is replaced with -1
f(-1) = 15*(1) + 10*(-1)
f(-1) = 15 - 10
f(-1) = 5

Therefore the answer is 5
7 0
3 years ago
Y is inversely proportional to a^3
Ludmilka [50]

Answer:

y = 0.64/x^3

Step-by-step explanation:

If y is inversely proportional to a^3, we can write the equation:

y * a^3 = k

Using a = 2 and y = 10, we have:

10 * 2^3 = k

k = 80

If a is directly proportional to x, we can write the equation:

a = c * x

Using x = 4 and a = 20, we have:

20 = c * 4

c = 5

Now, using the value of a = 5*x in the equation y * a^3 = 80, we have:

y * (5x)^3 = 80

y * 125x3 = 80

y = 80/(125x3) = 0.64/x^3

6 0
3 years ago
Naomi can text 90 words in 12 minutes. At this rate, how many minutes would it take her to text 165 words?
Nimfa-mama [501]

Answer:

Step-by-step explanation:

here cuhh

⠄⠄⠄⢰⣧⣼⣯⠄⣸⣠⣶⣶⣦⣾⠄⠄⠄⠄⡀⠄⢀⣿⣿⠄⠄⠄⢸⡇⠄⠄

⠄⠄⠄⣾⣿⠿⠿⠶⠿⢿⣿⣿⣿⣿⣦⣤⣄⢀⡅⢠⣾⣛⡉⠄⠄⠄⠸⢀⣿⠄

⠄⠄⢀⡋⣡⣴⣶⣶⡀⠄⠄⠙⢿⣿⣿⣿⣿⣿⣴⣿⣿⣿⢃⣤⣄⣀⣥⣿⣿⠄

⠄⠄⢸⣇⠻⣿⣿⣿⣧⣀⢀⣠⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⠄

⠄⢀⢸⣿⣷⣤⣤⣤⣬⣙⣛⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡍⠄⠄⢀⣤⣄⠉⠋⣰

⠄⣼⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢇⣿⣿⡷⠶⠶⢿⣿⣿⠇⢀⣤

⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣶⣥⣴⣿⡗

⢀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄

⢸⣿⣦⣌⣛⣻⣿⣿⣧⠙⠛⠛⡭⠅⠒⠦⠭⣭⡻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠄

⠘⣿⣿⣿⣿⣿⣿⣿⣿⡆⠄⠄⠄⠄⠄⠄⠄⠄⠹⠈⢋⣽⣿⣿⣿⣿⣵⣾⠃⠄

⠄⠘⣿⣿⣿⣿⣿⣿⣿⣿⠄⣴⣿⣶⣄⠄⣴⣶⠄⢀⣾⣿⣿⣿⣿⣿⣿⠃⠄⠄

⠄⠄⠈⠻⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⠄⣿⣿⡀⣾⣿⣿⣿⣿⣛⠛⠁⠄⠄⠄

⠄⠄⠄⠄⠈⠛⢿⣿⣿⣿⠁⠞⢿⣿⣿⡄⢿⣿⡇⣸⣿⣿⠿⠛⠁⠄⠄⠄⠄⠄

⠄⠄⠄⠄⠄⠄⠄⠉⠻⣿⣿⣾⣦⡙⠻⣷⣾⣿⠃⠿⠋⠁⠄⠄⠄⠄⠄⢀⣠⣴

⣿⣿⣿⣶⣶⣮⣥⣒⠲⢮⣝⡿⣿⣿⡆⣿⡿⠃⠄⠄⠄⠄⠄⠄⠄⣠⣴⣿⣿⣿

8 0
3 years ago
Read 2 more answers
Onique bought 2 hot dogs and 1 large soda. She spent $7. Scott
AlladinOne [14]
Hot dogs are $2.50 and drinks are $2.00
3 0
3 years ago
Other questions:
  • Which statements are true the ordered pair (1, 2) and the system of equations? y=−2x+47x−2y=3 HELP ASAP! WILL GIVE BRAINLIEST
    15·2 answers
  • Suppose these statements are true:
    9·2 answers
  • This year the fifth grade collected 216 fewer plastic containers than the fourth grade.How many plastic containers did the fifth
    5·1 answer
  • Each circle count as one whole write a mixed giving the amount shaded then. Write amount as an improper fraction
    8·1 answer
  • What is the answer to this question?
    6·1 answer
  • What is the solution 8x-3(2x-4)=3(x-6)
    7·2 answers
  • Which of the following is a rational number?
    7·1 answer
  • 7th grade math plss helpp
    12·2 answers
  • Whoever guesses my favorite color first gets brainliest
    10·2 answers
  • Round to 1000 and estimate the sum 11904+3808​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!