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
REY [17]
3 years ago
10

Complete the square to determine the minimum or maximum value of the function defined by the expression.

Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
3 0

The minimum value at -1 ⇒ D

Step-by-step explanation:

The completing square form of ax² + bx + c is a(x - h)² + k, where

  • h=\frac{-b}{2a}
  • k is the value of of the expression when x = h
  • k is minimum if a > 0 and maximum if a < 0

∵ The expression is x² + 4x + 3

∴ a = 1 , b = 4 , c = 3

- Use the rule above to find h

∵ h=\frac{-4}{2(1)}

∴ h = -2

- To find k substitute x by the value of h

∵ k = (-2)² + 4(-2) + 3 = 4 - 8 + 3

∴ k = -1

- Substitute h and k in the form of the completing square

∵ a(x - h)² + k = 1(x - -2)² + (-1)

∴ a(x - h)² + k = (x + 2)² - 1

∴ x² + 4x + 3 = (x + 2)² - 1

∵ The completing square is (x + 2)² - 1

∵ a = 1 ⇒ greater than zero

∴ The value is minimum

- The minimum value is the value of k

∵ k = -1

∴ The minimum value of the function is -1

The minimum value at -1

Learn more:

You can learn more about the quadratic function in brainly.com/question/9390381

#LearnwithBrainly

You might be interested in
how much simple interest is earned on an investment of $1250 if the money is invested for 5 years at an annual interest rate of
andrew-mc [135]
Approximately $307.73 is the total amount of interest earned for 5 years at an annual interest rate of 4.5%, with an initial investment of $1,250. 
7 0
3 years ago
Help I’m in 5th 14 question
shutvik [7]
You would be right with 26 because the absolute value of -30 is 30 then you subtract 56-30 and get 26 which is the remaining temp you need to get to 56.
3 0
2 years ago
Andy's ranch has 227 chickens living in their little houses. Each house has 8 chickens. How many little chicken houses does Andy
Murljashka [212]

Answer:

Step-by-step explanation:

sory I ain't know

3 0
3 years ago
Read 2 more answers
A cube made of an unknown material has a height of 9 cm. The mass of this cube is 3,645 grams. Calculate the density of this cub
garik1379 [7]

Answer:

Step-by-step explanation:

Volume of the cube = s^3

s = 9cm

V = 9 * 9 * 9

V = 729 cm^3

d = mass / volume

d = 3645 / 729

d = 5 grams / cm^3

4 0
3 years ago
HELPPP!!
sdas [7]
SOLUTION:
 

A box has a square base of side x and height y where x,y > 0.
Its volume is V = x^2y and its surface area is S = 2x^2 + 4xy.
(a) If V = x^2y = 12, then y = 12=x^2 and S(x) = 2x^2 C 4x (12=x2) = 2x2 + 48x^-1. Solve S'(x) = 4x - 48x-2 = 0 to obtain x = 12^1/3. Since S(x/) ---> infinite as x ---> 0+ and as x --->infinite, the minimum surface area is S(12^1/3) = 6 (12)^2/3 = 31.45, when x = 12^1/3 and y = 12^1/3.


(b) If S = 2x2 + 4xy = 20, then y = 5^x-1 - 1/2 x and V (x) = x^2y = 5x - 1/2x^3. Note that x must lie on the closed interval [0, square root of 10]. Solve V' (x) = 5 - 3/2 x^2 for x>0 to obtain x = square root of 30 over 3 . Since V(0) = V (square root 10) = 0 and V(square root 30 over 3) = 10 square root 30 over 9 , the maximum volume is V (square root 30 over 3) = 10/9 square root 30 = 6.086, when x = square root 30 over 3 and y = square root 30 over 3 .
5 0
2 years ago
Other questions:
  • Pat's ending balance on his debit card last month was $233.55. This month he had $542 worth of purchases and $710 worth of depos
    6·1 answer
  • The graphed line can be expressed by which equation?
    13·2 answers
  • If y varies directly as x, find the constant of variation if y= 34 when x= 2
    10·1 answer
  • A girl age is 28 years younger than her father the sum of their ages is 50 years find the ages of the girl and the father
    11·1 answer
  • PLEASE TRY TO HELP I'M STRUGGLING
    12·2 answers
  • 2. The 120 sixth graders are going on a
    10·1 answer
  • Write an equation for line p.
    14·1 answer
  • Help me plssss<br> Find m &lt; ABC.
    8·2 answers
  • PLEASE HELP!!!
    5·1 answer
  • Which statement is true? the equation –3|2x 1.2| = –1 has no solution. the equation 3.5|6x – 2| = 3.5 has one solution. the equa
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!