Use the graph of the polynomial
function to find the factored form of
its related polynomial. Assume it
has no constant factor
Answers
Answer:
The factored form of the polynomial is [tex]y = (x-2)\cdot (x+1)[/tex].
Step-by-step explanation:
According to the graph, we have a second order polynomial with a vertical axis of symmetry. The standard form of the polynomial is:
[tex]y = a\cdot x^{2}+b\cdot x + c[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficients.
We can obtain the solution of the polynomial by knowing three distinct points. From graph we know that the curve pass through the following three points: [tex](x_{1},y_{1}) = (-1, 0)[/tex], [tex](x_{2},y_{2}) = (0, -2)[/tex], [tex](x_{3},y_{3}) = (2,0)[/tex]. Three linear equations are constructed:
[tex]a^{2}-b+c = 0[/tex] (2)
[tex]c = -2[/tex] (3)
[tex]4\cdot a + 2\cdot b + c = 0[/tex] (4)
The solution of this system is [tex]a = 1[/tex], [tex]b = -1[/tex] and [tex]c = -2[/tex]. Then, the polynomial in standard form is [tex]y = x^{2}-x-2[/tex]. By factorization, we find that factored form is:
[tex]y = (x-2)\cdot (x+1)[/tex] (5)
Related Questions
After a 12% increase the cost of a new cooker is £190.40
Work out the original price of the cooker.
Answers
Answer:
1
X+.12*x=190.40
X(1+.12)=190.40
X=190.40/1.12=170
2a
X+x+25=100
2x=75
X=37.5%
Men=.375*270=101
2b
What is the slope-intercept form of the equation 8x + 7y - 2 - 0?
Answers
Answer:
y = -8x/7 + 2/7
Step-by-step explanation:
8x + 7y - 2 = 0
7y = -8x+2
y= (-8x + 2)/7
y = -8x/7 + 2/7
slope = -8/7, intercept = 2/7
If triangle DEF is dilated by a scale factor of 1/2 with center of dilation at the origin
(0,0), what is the x-coordinate of E'?
Please help 20 points
Answers
Answer:
(4,2)
Step-by-step explanation:
I am not able to see your screen well but these are the points that I saw in the beginning for E. 8,4. Your x value is either left or right and your y value is up and down. I saw 8 units right and 4 u it's up. Now your scale factor is 1/2. Remember if the scale factor is less than one the figure reduces. Our rule for dilations is (x,y) → (kx,ky). The scale factor is represented by K. Since your scale factor is 1/2 we know our triangle will reduce. Let's plug 1/2 in our x and y valued.
So E is (8,4). 8*1/2 is 4 and 4* 1/2 is 2. Are new points are E' (4,2).
On Monday the price for bottled water was six bottles for $17.88. on Saturday the price was three bottles for $9.33. which day had the higher unit price?
Answers
Answer:
saturday
Step-by-step explanation:
monday:
17.88 (price) divided by 6 (number of bottles) is equal to 2.98 (unit price per bottle)
saturday:
9.33 (price) divided by 3 (number of bottles) is equal to 3.11 (unit price per bottle)
can somebody help me please
Answers
B: (4,0)
C: (6,0)
Answer: your question is blurry
Step-by-step explanation:
Tomas bought 80 tickets for rides at an amusement park. Each ride costs 5 tickets, and Tomas has been on x rides so far. Select all the expressions that show the number of tickets that Thomas has left.
Answers
Answer:
What are the expressions do they tell you
Step-by-step explanation:
34 < 5x + 9 < 44
Inequality
Answers
Answer:
5 < x < 7
Step-by-step explanation:
- Move all terms not containing x from the center section of the inequality.
25 < 5 x < 35
- Divide each term in the inequality by 5 .
5 < 1x < 7
5 < x < 7
i hope this helps :)
can someone ease help me
Answers
Answer:
if the fraction is in missed then the answer is 34 but if not then it's 4
Answer:
2 1/8 X 16 = 42
Step-by-step explanation:
PLEASE HELP QUICKLY!!! I'll give Brainliest to the best answer.
Answers
Answer:
y4.5
Step-by-step explanation:
8/x = 32
..................
Answers
Answer:
Step-by-step explanation:
x= 1/4
The diameter of a circle measures 22 yd. What is the circumference of the circle?
Use 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer.
Answers
Answer:
69.08 yd
Step-by-step explanation:
22 times 3.14 = 69.08 yd
Find the simple interest paid and the amount paid for the loan.
$4800 at 9.9% for 4 years
Answers
Answer:
$1900.80
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 9.9%/100 = 0.099 per year,
then, solving our equation
I = 4800 × 0.099 × 4 = 1900.8
I = $ 1,900.80
The simple interest accumulated
on a principal of $ 4,800.00
at a rate of 9.9% per year
for 4 years is $ 1,900.80.
A person dove more than 100 feet below sea level.
Which value could represent the elevation, in feet, that the person dove?
A. -125
B. -50
C.60
D.150
please help i just have 10 minutes left
dont troll
Answers
Answer:
-125
Step-by-step explanation:
sea level is zero so cant be above that and the answer has to be below -100 and the only option is -125
Answer:
A -125
Step-by-step explanation:
because they went over 100ft below sea level
and if sea level is exactly 0 and they went under it over 100 the only option over 100 with a negative sign to show they went below sea level would be -125
Which expression is equivalent to
27x^2-72x/9x?
Assume that the denominator does not equal zero.
Answers
The expression that is equivalent to 27x² - 72x/9x is 3x - 8
How to determine the equivalent expression?The expression whose equivalence is to be determined is given as
27x^2-72x/9x
The above expression can be properly expressed as follows
27x² - 72x/9x
Introduce the use of brackets
So, we have
(27x² - 72x)/9x
Factor out x from the numerator
This gives
(27x² - 72x)/9x = x(27x - 72)/9x
Cancel out the common factor
(27x² - 72x)/9x = (27x - 72)/9
Factor out 9 from the numerator
This gives
(27x² - 72x)/9x = 9(3x - 8)/9
Cancel out the common factor
(27x² - 72x)/9x = 3x - 8
Hence, the equivalent expression is 3x - 8
Read more about equivalent expression at
https://brainly.com/question/15775046
#SPJ1
Urgent please!!! I really don’t understand it, tysm to anyone who can answer thissss :))))
(53 points)
Answers
Answer:
(ax + by + cz)/(a + b + c)Step-by-step explanation:
Average = Sum / NumberIn terms of the scores we calculate the sum as:
ax + by + czThe number is the sum of the frequencies:
a + b + cMean average score is:
(ax + by + cz)/(a + b + c)Please help me with this
Answers
Put one point at -10,6 and another at 6,-10
Pls help me with this question
B.y=3/4x-6
C.y=-6x+3/4
D.y=6x-3/4
Answers
Please help it's due today. Also if you don't know please don't answer.
Answers
I believe it's x= 20, hopes it help!
Answer:
x=20
Step-by-step explanation:
4 5 x
( 3 ) = 3
20 x
3 = 3
x = 20
What is the value of 3x^2– 7x + 9 when x = 4?
Answers
Answer:
29
Step-by-step explanation:
just substitute x with 4 in the equation :)
PLEASE HELP ANSWER ASAP I WILL GIVE BRAINLIEST
Mr. Peery has saved $150 to buy an iPhone 12. With his cell phone plan he can buy a new iPhone 12 for $200. If he can only save $10 a week how many weeks will it take for him to get enough money to buy the phone?
Create an equation for the problem here. Don't put any spaces.
How many weeks will it take?
Answers
Answer:
Let number of weeks be x
10x = 200-150
x=50/10
x=5
Thus it would take him 5 weeks to buy himself a iPhone12
Hope it helps
PLSSSSSS HELPPPPPPP FAST WILL GIVE BRAINLIEST
Answers
Answer:
The average number of points scored by a member of the team.
Step-by-step explanation:
The center of the data is another phrase for the mean of the data
Mean: the average of all data given (Add all the numbers up and divide by the amount of numbers there are).
Hope this helped :)
Answer:
I believe the answer would be A.
Step-by-step explanation:
You can get rid of B. and C. since it is in the middle. The highest would be at the top/right side and the lease would be at the bottom/left side. Then the total score does not make much sense because you would have to add up every number
A figure is dilated by a scale factor of 1
39
Explain whether the image is larger than,
smaller than, or the same size as the
original figure.
Answers
Responder:
Si el factor de escala de una figura es mayor que uno, la figura es mayor.
Explicación paso a paso:
Hará que la figura sea más grande porque si es menor que uno, la figura será menor. Por ejemplo, si el factor de escala es la mitad de la cifra, será la mitad más pequeña que la cifra original. Y si el factor de escala es 2, la figura será dos veces más grande que la figura original.
¡Espero que esto funcione!:)
Bruce flipped a penny 5 times. It landed on heads 2 times and tails 3 times. If he flips the coin a 6th time, what statement is true?
A. It is more likely to be heads.
BIt is equally likely to be heads or tails.
C. It is more likely to be tails.
D. It in not likely to be tails.
Answers
Answer:
B
Step-by-step explanation:
I would say B because they're only 2 options head and tails.
✩brainliest appreciated ✩
CAN SOMEONE HELP ME PLS I GIBE BRAINLIST AND POINTS
Answers
Answer:
184.26
Step-by-step explanation:
28.275 + 60 + 96 = 184.26
what is 2x + 7x + 8a + 9a
Answers
Answer: 9x + 17a
Step-by-step explanation:
2x + 7x + 8a + 9a
2x+7x= 9x
8a+9a= 17a
= 9x +17a
Answer:
9x + 17a
Step-by-step explanation:
9x + 17a. (A side note is that you can't add x and a together because they are different variables.)
Please help.
Algebra.
Answers
If a basketball was super inflated and had a rebound ratio of 85%, write an equation to determine what the height of the basketball would be after 6 bounces if it was dropped from a height of 10 ft.
Answers
Answer:
3.77ft
Step-by-step explanation:
According the question
The height of the basketball dropped from a height of 10ft after 6 bound having a rebound ratio of 85%
= 10(17/20)^6 = 3.77 feet
Find the measure of angle b
Answers
Answer:
48. ..........hhshhxhxx
Step-by-step explanation:
180-42-90=48
Use the rectangle shown to answer the question.
32 feet
8 feet
Stephanie dilated the rectangle and the dimensions of the image were 24
feet by 6 feet. What was the scale factor used? (In decimal form)
Answers
24/32= .75
6/8 = .75
Point A is located at (-2,-2). Plot all of the points 3 units away that have the same y-coordinate as point A.
Answers
Answer:
Points are ( 1, -2) , (-5, -2)
Step-by-step explanation:
the given point is A ( -2, -2)
If we fix the y coordinate , then we can change only x coordinate
As we want point 3 unit away
So, add 3 and subtract 3 from x coordinate to find the resultant point
If we add 3 to x coordinate , we get
-2 + 3 = 1
So the point be ( 1, -2)
If we subtract 3 to x coordinate , we get
-2 - 3 = -5
So the point be ( -5, -2)
The graph is as follows :