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
Semenov [28]
3 years ago
12

1.What is the shape of the graph of any quadratic function?

Mathematics
1 answer:
likoan [24]3 years ago
7 0

Answer:

Inverted parabola

Two complex solution

Step-by-step explanation:

any quadratic equation can be expressed in terms of ax^2 + bx + c = 0

It has two solutions which can be found using formula X =( -b + \sqrt{b^2 -4ac} )/2a \\or  \ ( -b - \sqrt{b^2 -4ac} )/2a

We know that  for any value inside the square root function

if it is positive its solution will be real number

for example  \sqrt{9} we can have two real solution -3 and 3

if it is negative its solution will be complex number

for example  \sqrt{-9}we can have two complex solution

expressed in term of a + ib or a - ib

------------------------------------------------------------------------------------------

Given in the problem

we have  ax^2 - bx + c

so its solution will be

X =( -(-b) + \sqrt{b^2 -4ac} )/2a \\or  \ ( -(-b) - \sqrt{b^2 -4ac} )/2a\\\\X =( b + \sqrt{b^2 -4ac} )/2a \\or  \ ( b - \sqrt{b^2 -4ac} )/2a\\

Since in this expression it is given in problem statement that b^2 - 4ac < 0 which will be a negative number and for negative number, its square root is complex number.

also X has two values as given above it will have two solution

hence it will have two complex solution based on above discussion.

Also for any quadratic equation shape of its curve if plotted on coordinate plane is parabolic.

If it has complex solution then curve of such expression  will not pass through X axis

You might be interested in
What is the value of x?​
Hatshy [7]

Answer:

x=84

Step-by-step explanation:

the sum of the angles in a pentagon is always 540 so do

540-131-108-107-110=84

8 0
2 years ago
Read 2 more answers
At basketball practice, charlie makes 52 baskets out of 80 shots. What percentage of baskets did he make?
Mazyrski [523]
Charlie made 65% of the baskets at practice
8 0
2 years ago
Read 2 more answers
Does there exist a di↵erentiable function g : [0, 1] R such that g'(x) = f(x) for all x 2 [0, 1]? Justify your answer
agasfer [191]

Answer:

No; Because g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R

Step-by-step explanation:

Assuming:  the function is f(x)=x^{2} in [0,1]

And rewriting it for the sake of clarity:

Does there exist a differentiable function g : [0, 1] →R such that g'(x) = f(x) for all g(x)=x² ∈ [0, 1]? Justify your answer

1) A function is considered to be differentiable if, and only if  both derivatives (right and left ones) do exist and have the same value. In this case, for the Domain [0,1]:

g'(0)=g'(1)

2) Examining it, the Domain for this set is smaller than the Real Set, since it is [0,1]

The limit to the left

g(x)=x^{2}\\g'(x)=2x\\ g'(0)=2(0) \Rightarrow g'(0)=0

g(x)=x^{2}\\g'(x)=2x\\ g'(1)=2(1) \Rightarrow g'(1)=2

g'(x)=f(x) then g'(0)=f(0) and g'(1)=f(1)

3) Since g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R

Because this is the same as to calculate the limit from the left and right side, of g(x).

f'(c)=\lim_{x\rightarrow c}\left [\frac{f(b)-f(a)}{b-a} \right ]\\\\g'(0)=\lim_{x\rightarrow 0}\left [\frac{g(b)-g(a)}{b-a} \right ]\\\\g'(1)=\lim_{x\rightarrow 1}\left [\frac{g(b)-g(a)}{b-a} \right ]

This is what the Bilateral Theorem says:

\lim_{x\rightarrow c^{-}}f(x)=L\Leftrightarrow \lim_{x\rightarrow c^{+}}f(x)=L\:and\:\lim_{x\rightarrow c^{-}}f(x)=L

4 0
3 years ago
Which of the following equations represents a quadratic relation?
iVinArrow [24]

Answer:

y=2x^2+1

Step-by-step explanation:

a quadratic equation has a x^2 term

4 0
2 years ago
Pls help …. Need it immediately ….
Leno4ka [110]

The answer is 10.73 years.

Here, the formula we can use is :

\boxed {Children = \frac{Boys+Girls}{2}} (for the average)

Substitute the values mentioned in the question.

10.54 = (10.35 + Girls)/2

21.08 = 10.35 + Girls

Girls = 10.73 years

3 0
2 years ago
Other questions:
  • And employee has a salary of $25,920 after a 4.2 to raise. What was the original salary
    6·1 answer
  • 100 a month for 48 months
    13·1 answer
  • Find the zeros of the function. f(x) = 3x^3 - 21x^2 + 36
    11·1 answer
  • Help plz !!!!!!!!!!!!!!!!!!!!!!!!!!
    7·1 answer
  • If Mike and Bill both push on the refrigerator, all BUT ONE statement would be true.
    7·1 answer
  • While chasing its prey, a cheetah is running slowly and then increases its speed by 50.6 miles per hour to reach a top speed of
    14·1 answer
  • What is 2 1/2 written as an improper fraction?
    10·1 answer
  • 2(1 - 5k) = 2k + 38<br> HURRY I NEED THIS ANSWER FAST
    12·1 answer
  • Giving brainliest *easy*
    5·1 answer
  • Please help asap.<br> I will give brainliest
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!