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
swat32
3 years ago
12

Given ​ f(x) = x^2 + 14x + 40 ​. Enter the quadratic function in vertex form in the box. f(x)=

Mathematics
2 answers:
finlep [7]3 years ago
6 0
Recall that the vertex form of a quadratic function (or parabolic function) is equal to

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

Now, given that we have f(x) = x² + 14x + 40, to express f into its vertex form, we must first fill in the expression to form a perfect square.

One concept that we must remember when completing the square is that

(a + b)² = a² + 2ab + b²

So, to complete the square for (x² + 14x + ____), we have 2ab = 14 where a = 1. Thus, b = 14/2 = 7. Hence, the last term of the perfect square must equal to 7² = 49.

So, going back to the function, we have

f(x) = (x^{2} + 14x + 40 + 0)
f(x) = (x^{2} + 14x + 40 + 49 - 49)
f(x) = (x^{2} + 14x + 49) + 40 - 49
f(x) = (x + 7)^{2} - 9

Thus, we have derived the vertex form of the function. 

Answer: f(x) = (x + 7)² - 9
Sindrei [870]3 years ago
3 0

Answer: f(x)=(x+7)^2-9. I took the test, I hope this helps you.

You might be interested in
Help please brainliest
serg [7]

Answer:

d.4x - 6

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Omg y'alls! MOre MaTh, and it is the LAST OF IT!
BARSIC [14]

Answer:

non-linear and increasing.

Step-by-step explanation:

We know it is non-linear simply because it is not a straight line. And the numbers in the equations tell us it is increasing not deceasing.

4 0
3 years ago
Read 2 more answers
Need help for 12 please​
igomit [66]

Ummmm where is it? I dont see 12

8 0
2 years ago
Which expressions are equivalent to 2-(-6+3)+4c
Artyom0805 [142]

Answer:

c. none of the above

Step-by-step explanation:

(-6+3)= -3

2--3=2+3=5

5+4c cant add them since they arent like terms

final answer 5+4c and that option isnt here

3 0
2 years ago
the providence children muesuem installed a fence around the perimeter of the propety. the propety is a rectangle. one side is 3
mash [69]
Its a rectangle so two sides are equal and both sides that are opposite of each other are equal. So two sides are 37. Then you add them together to get 74, then subtract it from 164 to get 90 the rest of the fence length. Then divide it by two to get 45 which is the other side lengths, so it would be a 37 by 45 rectangle one side would be 37 while the other two are 45.
7 0
3 years ago
Other questions:
  • Find the distance between (-1, 4) and (3, 1).
    9·2 answers
  • Solve 38x21 using an area model
    11·1 answer
  • How is 88 a solution to 18x11
    9·1 answer
  • Divide the ratio of 30 in the ratio of 4:2
    11·2 answers
  • I need help please<br> Thank you
    12·2 answers
  • 3 ways to write the ratio 6 dogs to 5 cats.*
    8·2 answers
  • HELP PLEASE ASAP. NO LINKS OR I WILL REPORT​
    10·1 answer
  • Answer correctly and fast please.
    14·1 answer
  • If 4x = 28, find the value of 29 - 5x
    5·2 answers
  • The price of a TV-set is $480. If it goes on sale at 18% off what will be the new price?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!