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
Vika [28.1K]
3 years ago
10

Complete the square to find the minimum value of the expression 4x2 + 8x + 23.

Mathematics
1 answer:
Tcecarenko [31]3 years ago
3 0
So you need to come up with a perfect square that works for the x coefficients.
like.. (2x + 2)^2
(2x+2)(2x+2) = 4x^2 + 8x + 4
Compare this to the equation given. Our perfect square has +4 instead of +23. The difference is: 23 - 4 = 19

I'm going to assume the given equation equals zero..

So, If we add subtract 19 from both sides of the equation we get the perfect square.

4x^2 + 8x + 23 - 19 = 0 - 19
4x^2 + 8x + 4 = - 19
complete the square and move 19 over..
(2x+2)^2 + 19 = 0
factor the 2 out becomes 2^2 = 4
ANSWER: 4(x+1)^2 + 19 = 0

for a short cut, the standard equation
ax^2 + bx + c = 0 becomes a(x - h)^2 + k = 0
Where "a, b, c" are the same and ..
h = -b/(2a)
k = c - b^2/(4a)

Vertex = (h, k)
this will be a minimum point when "a" is positive upward facing parabola and a maximum point when "a" is negative downward facing parabola.


You might be interested in
600 x 800...................................
Mashcka [7]
First do 6×8=48, then just add the 0's to the end to get 480,000
6 0
3 years ago
Read 2 more answers
X - (-20) = 5 _________________
tamaranim1 [39]

X - (-20) = 5

When you subtract a negative, change it to addition:

X + 20 = 5

Subtract 20 from both sides:

X = -15

8 0
3 years ago
Read 2 more answers
How many solutions does the equation −5a + 5a + 9 = 8 have?
faust18 [17]

Answer: the answer will be none

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Please help!!! 25 points!<br> Which of these numbers are irrational?
Aleks04 [339]

I belive that b is the answer.

3 0
3 years ago
Zaire, Manny, Richard, Navid and Gregory found a rope that was 271.5 feet long. If they cut the rope into equal pieces, what was
posledela

Answer:

43.5

Step-by-step explanation:

217.5/5

43.5

4 0
3 years ago
Other questions:
  • What is 4+2 x { 16/ (5+3)} 2
    6·2 answers
  • For a normally distributed random variable x with m = 75 and s = 4, find the probability that 69 &lt; x &lt; 79 Use the table to
    7·1 answer
  • 9/10 minus 5/9 equals
    15·2 answers
  • For any triangle, the sum of the measure of the three angles equals 180 degrees. Two of the angles have the same measure,a,and t
    8·1 answer
  • A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample
    7·1 answer
  • If x represents the amount Rita earns each week, which expression represents the amount she earns in a year?
    10·2 answers
  • Perform the indicated operations and simplify:<br> 8c + 5c - (5c+6)
    8·1 answer
  • MATH QUESTION PLEASE HELPPP ASAP, DUE IN AN HOUR
    8·1 answer
  • I will give many points and brainlest if you find the area of the polygon
    6·1 answer
  • Zach can run 7 1/2 miles in 1 1/2 hours find the average speed in miles per hour
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!