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
maria [59]
2 years ago
6

Hector used the quadratic formula to solve the polynomial equation

Mathematics
2 answers:
Komok [63]2 years ago
7 0

Answer:

8

Step-by-step explanation:

ax² + bx + c = 0

In the quadratic formula the "b" coefficent gets sqaured

bx = 8x

b = 8

Virty [35]2 years ago
5 0

Answer:

STEP

1

:

Equation at the end of step 1

 (32x2 -  8x) -  2  = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1     Factoring  9x2-8x-2

The first term is,  9x2  its coefficient is  9 .

The middle term is,  -8x  its coefficient is  -8 .

The last term, "the constant", is  -2

Step-1 : Multiply the coefficient of the first term by the constant   9 • -2 = -18

Step-2 : Find two factors of  -18  whose sum equals the coefficient of the middle term, which is   -8 .

     -18    +    1    =    -17

     -9    +    2    =    -7

     -6    +    3    =    -3

     -3    +    6    =    3

     -2    +    9    =    7

     -1    +    18    =    17

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

2

:

 9x2 - 8x - 2  = 0

STEP

3

:

Parabola, Finding the Vertex:

3.1      Find the Vertex of   y = 9x2-8x-2

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 9 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   0.4444  

Plugging into the parabola formula   0.4444  for  x  we can calculate the  y -coordinate :

 y = 9.0 * 0.44 * 0.44 - 8.0 * 0.44 - 2.0

or   y = -3.778

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = 9x2-8x-2

Axis of Symmetry (dashed)  {x}={ 0.44}

Vertex at  {x,y} = { 0.44,-3.78}

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-0.20, 0.00}

Root 2 at  {x,y} = { 1.09, 0.00}

Solve Quadratic Equation by Completing The Square

3.2     Solving   9x2-8x-2 = 0 by Completing The Square .

Divide both sides of the equation by  9  to have 1 as the coefficient of the first term :

  x2-(8/9)x-(2/9) = 0

Add  2/9  to both side of the equation :

  x2-(8/9)x = 2/9

Now the clever bit: Take the coefficient of  x , which is  8/9 , divide by two, giving  4/9 , and finally square it giving  16/81

Add  16/81  to both sides of the equation :

 On the right hand side we have :

  2/9  +  16/81   The common denominator of the two fractions is  81   Adding  (18/81)+(16/81)  gives  34/81

 So adding to both sides we finally get :

  x2-(8/9)x+(16/81) = 34/81

Adding  16/81  has completed the left hand side into a perfect square :

  x2-(8/9)x+(16/81)  =

  (x-(4/9)) • (x-(4/9))  =

 (x-(4/9))2

Things which are equal to the same thing are also equal to one another. Since

  x2-(8/9)x+(16/81) = 34/81 and

  x2-(8/9)x+(16/81) = (x-(4/9))2

then, according to the law of transitivity,

  (x-(4/9))2 = 34/81

We'll refer to this Equation as  Eq. #3.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-(4/9))2   is

  (x-(4/9))2/2 =

 (x-(4/9))1 =

  x-(4/9)

Now, applying the Square Root Principle to  Eq. #3.2.1  we get:

  x-(4/9) = √ 34/81

Add  4/9  to both sides to obtain:

  x = 4/9 + √ 34/81

Since a square root has two values, one positive and the other negative

  x2 - (8/9)x - (2/9) = 0

  has two solutions:

 x = 4/9 + √ 34/81

  or

 x = 4/9 - √ 34/81

Note that  √ 34/81 can be written as

 √ 34  / √ 81   which is √ 34  / 9

Solve Quadratic Equation using the Quadratic Formula

3.3     Solving    9x2-8x-2 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

                                   

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     9

                     B   =    -8

                     C   =   -2

Accordingly,  B2  -  4AC   =

                    64 - (-72) =

                    136

Applying the quadratic formula :

              8 ± √ 136

  x  =    —————

                   18

Can  √ 136 be simplified ?

Yes!   The prime factorization of  136   is

  2•2•2•17

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 136   =  √ 2•2•2•17   =

               ±  2 • √ 34

 √ 34   , rounded to 4 decimal digits, is   5.8310

So now we are looking at:

          x  =  ( 8 ± 2 •  5.831 ) / 18

Two real solutions:

x =(8+√136)/18=(4+√ 34 )/9= 1.092

or:

x =(8-√136)/18=(4-√ 34 )/9= -0.203

Two solutions were found :

x =(8-√136)/18=(4-√ 34 )/9= -0.203

x =(8+√136)/18=(4+√ 34 )/9= 1.092

Step-by-step explanation:

You might be interested in
What are two numbers that when multiplied equal -2, and also when added equals 1
lara [203]
Two numbers that multiply to -2 could be

-1 and 2

Or

-2 and 1.

Since -1+2=1, -1 and 2 are the numbers you are looking for.

Hope this helps!
4 0
3 years ago
Read 2 more answers
The middle of the skate ramp is 2.5 meters wide. Emelia and her father want to use a board that is 23.5 decimeters long. Is this
Vinvika [58]

Answer:

it's 1 dekameter (dam) = 10 meters you need to use that

4 0
2 years ago
I need help on a mathematics question. I need an explanation.
romanna [79]
Start by dividing both sides by 2 to get log(x)= \frac{1}{2}log(64).  Doing the math on the right, keeping in mind that logs have an unwritten base of 10, gives us log_{10} (x)=.903089987.  Rewriting this in exponential form is 10^{.903089987}=x.  That means that x = 8.  Not negative, only positive.
4 0
3 years ago
Which statement must be true?
poizon [28]
Vs<vu
cause smaller sides have smaller angels in front ofthem
4 0
3 years ago
Read 2 more answers
Find the area. If applicable, leave the answer in simplest radical form. Helpp​
inna [77]

Answer:

The area is 28\ m^{2}

Step-by-step explanation:

I assume that the figure is a square

The area of a square is equal to

A=b^{2}

where

b is the length side of the square

In this problem we have

b=2(\sqrt{7})=2\sqrt{7}\ m

substitute in the formula

A=(2\sqrt{7})^{2}

A=28\ m^{2}

6 0
3 years ago
Other questions:
  • Without parentheses the expression 8+30 dividend by 2+4 equals 27. Place parentheses in the expression so that it equals 12; the
    11·1 answer
  • What is the simplest form of 7/10 + 1/5
    12·2 answers
  • What is the law of sllyogism in symbolic form?
    7·1 answer
  • Chang knows one side of a triangle is 13 cm Which set of two sides is possible for the lengths of the other two sides of this
    8·1 answer
  • H is a discrete-time LTI system with impulse response h[n] = δ[n] − 2δ[n − 1] + 3δ[n − 2]. Find the output signal y[n] in terms
    15·1 answer
  • What is the cost to drive a 2020 honda civic ?
    8·1 answer
  • this is step three of mathematical induction can somebody help me solve the rest, you only work on the left side to make it equa
    9·1 answer
  • Do -24 and -24 cancel each other out
    7·1 answer
  • You bought a shirt for $13.50 that was originally $45.00. In terms of percent, what discount did you get on the shirt?
    7·1 answer
  • What is the volume of the prism with the dimensions given below? <br><br> 2/3m 1 1/8m 3 3/4m
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!