What is the equation, In factored form, of the quadratic function shown in the graph?
Answers
Given:
The graph of a quadratic function.
To find:
The equation of the quadratic function in factored form.
Solution:
From the given graph it is clear that the graph of the function intersect the x-axis at point (-3,0) and (2,0).
Since -3 and 2 are the zeros of the function, therefore (x+3) and (x-2) are the factors of the required quadratic function.
Now, the function can be written as:
[tex]f(x)=a(x+3)(x-2)[/tex] ...(i)
The graph of the function intersect the y-axis at (0,-6). Substituting [tex]x=0,f(x)=-6[/tex] in (i), we get
[tex]-6=a(0+3)(0-2)[/tex]
[tex]-6=a(3)(-2)[/tex]
[tex]-6=-6a[/tex]
[tex]\dfrac{-6}{-6}=a[/tex]
[tex]1=a[/tex]
Substituting [tex]a=1[/tex] in (i), we get
[tex]f(x)=1(x+3)(x-2)[/tex]
Therefore, the required function is [tex]f(x)=1(x+3)(x-2)[/tex].
Related Questions
Solve for x. Round to the nearest tenth, if necessary.
Answers
Answer:
x = 10.7
Step-by-step explanation:
We have:
[tex]\frac{x}{sin 90}[/tex] = [tex]\frac{9.2}{sin59}[/tex]
=> x × sin59 = 9.2 × sin90
=> x × sin59 = 9.2
=> x = 9.2 ÷ sin59
=> x = 10.733027...
=> x = 10.7 (Round to the nearest tenth)
<3 Have a nice day!!
I need help, I can’t figure out the answer
Answers
Answer:
Step-by-step explanation:
in negative exponents you should switch both numerator and denominator so for 2 raised to -1 you should switch the numerator and denominator and it will become 1/2 in which 2 is raised to power 1
you can do the same for the remining sums
so a is 1/2 in which 2 is raised to 6 so answer is 1/64
WILL MARK AS BRAINLIEST. PLS HLP MEEE
Answers
I need this solve really fast.
Which sequences are geometric? Select three options.
Answers
Answer:
I guess this is the answer
Answer:
1 2 and 4 not capping like everyone else
Step-by-step explanation:
the quiz sequence
Prove algebraically that n^2-2-(n-2)^2 is always even
Answers
Answer:
It is even because it is equal to 2(2n-3) so you can divide it by two and get (2n-3)
Step-by-step explanation:
[tex] {n}^{2} - 2 - ( {n}^{2} + 4 - 4n) = \\ {n}^{2} - 2 - {n}^{2} - 4 + 4n = \\ 4n - 6 = 2(2n - 3)[/tex]
Step-by-step explanation:
A new hospital tracked the number of births during its first 6 months of operation, as shown in the table.
A 2-column table with 6 rows. The first column is labeled month with entries 1, 2, 3, 4, 5, 6. The second column is labeled number of births with entries 137, 110, 93, 70, 65, 77.
Find a quadratic function that models the data. Round numerical values to the nearest whole number
Answers
Answer:
y = 4x² - 43x + 178
Step-by-step explanation:
Given that data:
1 __ 137
2 __ 110
3 __ 93
4 __ 70
5 __ 65
6 __ 77
Usibg technology, the quadratic regression equation obtained is written in the form:
Ax² + Bx + C
A = 4.34 = 4 ( nearest whole number)
B = - 43.46 = - 43 (nearest whole number)
C = 178.3 = 178 ( nearest whole number)
Hence, the quadratic model is
y = 4x² - 43x + 178
By rounding the coefficients to the nearest whole number, the quadratic function that models the data is[tex]f(x) = 5x^2 - 42x + 174[/tex]
How to Find a quadratic function that models the data.To find a quadratic function that models the data, use a quadratic equation of the form:
[tex]f(x) = ax^2 + bx + c[/tex]
Let's use the given data points to form a system of equations and solve for the coefficients a, b, and c.
Using the first data point (month 1 with 137 births):
[tex]f(1) = a(1)^2 + b(1) + c = 137[/tex]
a + b + c = 137 (Equation 1)
Using the second data point (month 2 with 110 births):
[tex]f(2) = a(2)^2 + b(2) + c = 110[/tex]
4a + 2b + c = 110 (Equation 2)
Using the third data point (month 3 with 93 births):
[tex]f(3) = a(3)^2 + b(3) + c = 93[/tex]
This simplifies to:
9a + 3b + c = 93 (Equation 3)
Solve this system of equations will give us the values of a, b, and c.
Subtract Equation 1 from Equation 2
3a + b = -27 (Equation 4)
Subtract Equation 1 from Equation 3
8a + 2b = -44 (Equation 5)
Now solve Equations 4 and 5 simultaneously.
Multiply Equation 4 by 2 and subtracting it from Equation 5:
8a + 2b - (6a + 2b) = -44 - (-54)
2a = 10
Divide both sides by 2:
a = 5
Now substitute the value of a back into Equation 4:
3(5) + b = -27
15 + b = -27
Subtract 15 from both sides:
b = -42
Finally, substitute the values of a and b into Equation 1
5 + (-42) + c = 137
-37 + c = 137
Add 37 to both sides:
c = 174
Therefore, the quadratic function that models the data is:
[tex]f(x) = 5x^2 - 42x + 174[/tex]
Rounding the coefficients to the nearest whole number, the quadratic function becomes:
[tex]f(x) = 5x^2 - 42x + 174[/tex]
Learn more on quadratic on https://brainly.com/question/1214333
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The quotient of (x -3x3-3x2 - 10x + 15) and a polynomial is (x2-5). What is the polynomial?
Answers
Answer:
(-3x -3 - 24x/(x²-5))
Step-by-step explanation:
(x - 3x³ - 3x² - 10x + 15) / p = x² - 5
(-3x³ - 3x² - 9x + 15) / p = x² - 5
p = (-3x³ - 3x² - 9x + 15)/(x² - 5) = -3x - 3 - 24x/(x² - 5)
- -3x³ + 15x
---------------------------------
0 - 3x² - 24x + 15
- - 3x² + 15
‐-----------------------------------
0 - 24x + 0
Helppppp pls and thankyouuu
Answers
Answer:
20 minutes on the stationary bike
10 minutes on the treadmill
Step-by-step explanation:
x = minutes on bike
y = minutes on treadmill
x + y = 30
12x + 15y = 390
x = 30-y
12(30-y) + 15y = 390
360 - 12y + 15y = 390
3y = 30
y = 10
x + 10 = 30
x = 20
find the area and perimeter of a circle
Answers
Answer:
Step-by-step explanation:
r=5 cm
area=πr²
perimeter=2πr
substitute the value of r and calculate.
Answer:
78.54 [tex]cm^{2}[/tex] Area
31.42 cm Circumference/perimeter
Step-by-step explanation:
A = [tex]\pi r^{2}[/tex]
C = 2[tex]\pi[/tex]r
A = [tex]\pi[/tex][tex]5^{2}[/tex]
A = 25[tex]\pi[/tex]
A = 78.54
C = 2[tex]\pi[/tex](5)
C = 10[tex]\pi[/tex]
C = 31.42
charlie drove 208 miles in 4 hours at a constant speed He continues at that speed give the equation that shows the relationships between driving hours and mies driven
Answers
Answer:
M = 52* H
"miles equals 52 times hours driven"
Step-by-step explanation:
A triangle has sides with lengths of 60 yards, 80 yards, and 100 yards. Is it a right triangle?
Answers
yes, it's a scaled version of a triangle with side lengths 3, 4 and 5.
by a factor of 20
a triangle with side lengths 3, 4 and 5 is a right triangle and it holds true for a²+b²=c², because 9+16=25
the 3,4,5-triangle is the simplest right triangle to calculate it's numbers seem somehow elegant.
the triangle in your problem is just a bigger version of it (wich means all angles stay the same).
My reasoning is lacking, but I'm sure
Which of the Following best describes a cylinder?
Answers
Answer:
D
Step-by-step explanation:
all the options seems similar..but i can find the D more suitable
if demand is 75 lakh setup and holding cost is 29 and 35 number of piece per order is 2.3 lakh printing is done 300 days and delivery within 2 days what is eoq
Answers
A
64 :) i think
Step-by-step explanation:
what is lockdown
what is lockdown
Answers
Answer:
lockdown is a restriction policy for people or community to stay where they are, usually due to specific risks to themselves or to others if they can move and interact freely.
lockdown is when a country or a state closes and prevent entry or exit from one state or country to another in order to avoid the spread of for example a disease.
A man and his wife share a lottery prize of $1 500 000 in the ratio of 41:34. What is the difference between the man's share and his wife's share
Answers
Answer:
$140,000
Step-by-step explanation:
Value of lottery = $1,500,000
Man's ratio = 41
Wife's ratio = 34
Total ratio = 41 + 34 = 75
Man's share = Man's ratio / Total ratio * Value of lottery
= 41/75 * $1,500,000
= 0.5466666666666 * $1,500,000
= $820,000
Wife's share = wife's ratio / total ratio * Value of lottery
= 34/75 * $1,500,000
= 0.4533333333333 * $1,500,000
= $680,000
Difference between the man's share and his wife's share
= Man's share - wife's share
= $820,000 - $680,000
= $140,000
what is the solution to log_5 (10x-1)=log_5 (9x+7)
a) x= 6/19
b) x= 8/19
c) x=7
d) x=8
Answers
Answer: D
To solve the equation we proceed as follows:
log5(10x-1)=log5(9x+7)
canceling out log5 we get:
(10x-1)=(9x+7)
solving for x we get:
10x-9x=7+1
x=8
thus the value of x=8
Step-by-step explanation:
it was on brainly already
Create an entertaining presentation of your choice that will help students
remember how to add and subtract integers.
Answers
Answer:
maybe you can give them a simple example.
use what they are interested for.
for example if he or she love playing basketball.
you can draw three white ball, if other give you two ball, you can draw two balls. instead, if other want to borrow four balls from you, then you can draw four balls to black and count the left balls.
hope it can help you!!
Step-by-step explanation:
BRAINLIEST FOR CORRECT ANSWER
Answers
Answer:
y=-2x+6
Step-by-step explanation:
For this question, you need the slope-intercept form which is y=mx+b, where m is the slope and b is the y-intercept. We should first find the slope of the equation. The slope is the rise-over-run; this means that the slope is equal to the difference in y over x. One way to find the slope is to count the difference between the two coordinates or you can use the formula. Either way, the y decreases by 2, and the x increases by 1. Therefore, the slope is -2.
Then, find the intercept. One way to do this by plugging in one of the coordinates into the equation we have so far, y=-2x+b. So, plug 4 in for y and 1 in for x; 4=-2(1)+b. Next, solve for b. This equals b=6.
Finally, plug in the slope and intercept for the final answer, y=-2+6.
common denominator for 3/4 and 7/6
Answers
Answer:
12
Step-by-step explanation:
3/4 = 9/12
7/6 = 14/12
12 is a suitable common denominator for these fractions.
__
4 = 2·2
6 = 2·3
The common denominator must include all these factors (and no more than necessary), so must be ...
LCD = 2·2·3 = 12
(d) 23.89 cg = ______________ Kg
Answers
Answer:
the answer is 0.0002 kilograms
Step-by-step explanation:
(05.05 HC)The four points (−2, 5), (−2, −1), (5, −1), and (3, 5) are the vertices of a polygon. What is the area, in square units, of this polygon? 27 units2 33 units2 36 units2 51 units2
Answers
Answer:
Area = 36 squ. unit
Step-by-step explanation:
According to the Question,
Given That, The four points (−2, 5), (−2, −1), (5, −1), and (3, 5) are the vertices of a polygon. (Please find diagram in attachment)by using these points a quadrilateral is formed with two opposite sides 7 and 5 and with height 6 (Refer in the diagram).
Therefore, the area of this polygon isArea = 1/2 * (sum of opposite side) * height
Area = 1/2 * (7+5) * 6
Area = 3*12
Area = 36 squ. unit
Answer:
36
Step-by-step explanation:
An x-method chart shows the product a c at the top of x and b at the bottom of x. Below the chart is the expression a x squared + b x + c. What are the factors of x2 – 144? And
Answers
Answer:
[tex](x -12)(x + 12)[/tex]
Step-by-step explanation:
Given
See attachment for chart
Required
The factors of [tex]x^2 - 144[/tex]
First, express [tex]x^2 - 144[/tex] as [tex]ax^2 + bx + c[/tex]
So, we have:
[tex]x^2 - 144 = x^2 + 0x - 144[/tex]
Compare the above expression to: [tex]ax^2 + bx + c[/tex]
We have:
[tex]ax^2 + bx + c = x^2 + 0x - 144[/tex]
So:
[tex]a =1[/tex]
[tex]b =0[/tex]
[tex]c = -144[/tex]
and
[tex]a * c = d * e[/tex]
Calculate ac
[tex]a* c = 1 * -144[/tex]
[tex]a* c = -144[/tex]
Rewrite as:
[tex]a* c = -12 * 12[/tex]
Recall that:
[tex]a * c = d * e[/tex]
Hence:
[tex]d = -12; e = 12[/tex]
So, on the x chart, we have:
ac
d e
b
This gives:
-144
-12 12
0
The factors are
[tex](x + d)(x + e)[/tex]
[tex](x -12)(x + 12)[/tex]
Answer:
✔ (x – 12)
and
✔ (x + 12)
Step-by-step explanation:
whats the function for y=-4x+3
Answers
Answer:
the function for y=-4x+3
= soln,
y=mx+b"
The table shows the height of water in a pool as it is
being filled
The slope of the line through the points is 2. Which
statement describes how the slope relates to the
height of the water in the pool?
Height of Water in a Pool
Time
(min)
2
4
6
8
10
Height
(in.)
8
12
16
20
24
The height of the water increases 2 inches per
minute.
The height of the water decreases 2 inches per
minute.
The height of the water was 2 inches before any
water was added.
The height of the water will be 2 inches when the
pool is filled.
Answers
Answer:
Step-by-step explanation:
Slope is the rate of change. For us, this rate of change is inches of water per minute. If this rate of change is 2/1, that means that the rate is changing 2 inches every minute (aka The height of the water increases 2 inches per minute, first choice in your list of possibilities).
Help me solve for 20 please ok?
Answers
Answer:
option c
Step-by-step explanation:
Quadratic function f(x) = ax² + bx +c
Here the the co-efficient of x, that is a tells if the graph is wider or narrower.
1) a < 1 that is if a is decimal less than 1, then the graph is wider.
2) a > 1, then the graph is narrow.
the sum of the first n terms of a sequence is 20 - 10 / 2 ^ n - 1 find the sum of the first five terms
Answers
Answer:
[tex]S_5=\dfrac{170}{9}[/tex]
Step-by-step explanation:
Given that,
The sum of first n term of a sequence is[tex]S_n=20-\dfrac{10}{2n-1}[/tex]
We need to find the sum of the first 5 terms.
Put n = 5,
[tex]S_5=20-\dfrac{10}{2(5)-1}\\\\=20-\dfrac{10}{10-1}\\\\=20-\dfrac{10}{9}\\\\=\dfrac{170}{9}[/tex]
So, the sum of first 5 terms is equal to [tex]\dfrac{170}{9}[/tex].
Help,anyone can help me do quetion,I will mark brainlest.
Answers
Answer:
Area of a triangle=1/2×base x height
Let y represent the height
50cm²=1/2×20cm×y
50cm²=10cm×y
50cm²/10cm=10cm×y/10cm
5cm=y
therefore the height of the triangle is 5cm
Area of a trapezoid=1/2×a+b×height
let h represent the height
42cm²=(1/2×14cm+7cm)×h
42cm²=1/2×21cm×h
42cm²=21cm×h/2
42cm²×2=21cm×h(cross multiply)
84cm²=21cmh
84cm²/21cm=21cmh/21cm
4cm=h
Therefore the height is 4cm
For f (x) - 4x +1 and g(x) = ? -5, find (fºg)(4).
Answers
[tex](f\circ g)(x)=f(g(x))=4(x^2-5)+1=4x^2-19[/tex]
[tex](f\circ g)(4)=4\cdot4^2-19=64-19=\boxed{45}[/tex]
Hope this helps.
What did I do wrong in notes, and why is the answer what it shows on screenshot
Answers
Answer:
Hope you find it helpful and usef
Mia invests $5,000 in an index fund. After 1 year, the fund's share price has increased by 8%. How much did Mia gain?
Answers
Answer: In the end, she has $5400 in total, so she must gain $400 on her investment.
Step-by-step explanation:
8% is 0.08 >>> add 1 to it = 1.08
5000*1.08 = 5400
or the other way to do this is 5000*0.08 = 400 and then 5000+400=5400
Hope this helps!