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
Andre45 [30]
3 years ago
11

Let b be a real number. For what value of b does the function f(x)=x^2-2bx+(b^2+2b-1) have one and only one x-intercept?

Mathematics
1 answer:
Leokris [45]3 years ago
6 0

Answer:

b =  \frac{1}{2}

Step-by-step explanation:

Using the discriminant for nature of roots ( x- intercepts )

If b² - 4ac = 0 then roots are real and equal ( that is only 1 x- intercept )

Given

f(x) = x² - 2bx + b² + 2b - 1

with a = 1, b = - 2b and c = b² + 2b - 1, then

(- 2b)² - 4(b² + 2b - 1) = 0 ← distribute and simplify left side

4b² - 4b² - 8b + 4 = 0

- 8b + 4 = 0 ( subtract 4 from both sides )

- 8b = - 4 ( divide both sides by - 8 )

b = \frac{1}{2}

You might be interested in
Please help i don’t understand
olganol [36]

9514 1404 393

Answer:

  3

Step-by-step explanation:

Vertical angles share a vertex point, and have opposite rays for sides. In short, they are across the point of intersection from each other. Vertical angles do not have a common side (they are <em>not</em> adjacent).

The first part of the problem is to identify angle NCA. That is shown in red in the attachment. The vertical angle is across the point of intersection. It is angle 3.

5 0
3 years ago
HELP ME I WILL GUVE BRAINLEST PLEASE THE ITHER GUY DID IT WRONG
laila [671]
Uppose the fence was 350 ft from home plateAt what height was each ball when it

over the ?
4 0
2 years ago
What is40.99 times 2.1
inessss [21]

Answer:

40.99* 2.1= 86.079

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Every day Amy travels 30 miles one-way to work. The park-and-ride where she catches the train is 5 miles from her home. The aver
sukhopar [10]

Answer:

26

Step-by-step explanation:

3 0
3 years ago
How many dimensions exists in the universe?<br>A) 3<br>B) 5<br>C) 11<br>D) 10
nalin [4]
Your answer is 10
<span>1. Length
</span><span>2. Height
</span><span>3. Depth
</span><span>4. Time
</span><span>5. Possible Worlds
</span><span>6. A Plane of All Possible Worlds With the Same Start Conditions
</span><span>7. A Plane of All Possible Worlds With Different Start Conditions
</span><span>8. A Plane of All Possible Worlds, Each With Different Start Conditions, Each Branching Out Infinitely
</span><span>9. All Possible Worlds, Starting With All Possible Start Conditions and Laws of Physics
</span><span>10. Infinite Possibilities</span>
5 0
3 years ago
Other questions:
  • the regular price of a stellar 9 video game is 44.50, but it's on sell for a 30% discount , what's the discount , what's the sal
    11·1 answer
  • David purchased three shirts that cost an equal price as well as a hat for $15. If he spent $47.52 shopping, write an equation t
    14·1 answer
  • A 10 foot tree casts a 4.5 foot shadow.
    14·2 answers
  • to make a set for a stage, you bought a piece of lumber 9 feet long. How many 2 1/4 foot pieces can you cut from this piece of l
    15·1 answer
  • How do u add 2 3/4 + 3 3/8
    11·2 answers
  • Which math operation determines the following recursive sequence!
    7·2 answers
  • 4 – 2( x – 3 ) = 2 4
    15·2 answers
  • If a = b /c-b , find the value of b when a = 3 and c = 10 *
    7·1 answer
  • 8) A box of 12 light bulbs fell
    6·1 answer
  • Using standard form, write
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!