Answers
Given:
The graph of a quadratic function [tex]y=x^2-4x+3[/tex].
To find:
(a) The coordinates of the turning point.
(b) The roots of the equation [tex]y=x^2-4x+3[/tex]
Solution:
(a)
From the given graph it is clear that first the graph is decreasing after that it is increasing. So, the minimum point is the turning point.
The turning is at (2,-1) because the distance between the turning point from the y-axis is 2 and from the x-axis is 1 in the downward direction.
Therefore, the coordinates of the turning point are (2,-1).
(b)
The x-intercepts are the roots of an equation because roots are the x-coordinates of the points where the graph intersect the x-axis.
From the given graph it is clear the graph intersect the x-axis at x=1 and x=3.
Therefore, the roots of the given equation are 1 and 3.
Related Questions
PLEASE HELP!!
if y(x) = 5x-2 and g(x) = 2x + 1, find (f + g)(x).
Answers
Answer:
(f + g)(x) = 7x - 1
Step-by-step explanation:
Given : f(x) = 5x – 2 and g(x) = 2x + 1
We have to find (f + g)(x)
Consider (f + g)(x) = f(x) + g(x)
Also, given f(x) = 5x – 2 and g(x) = 2x + 1
Substitute, we have,
f(x) + g(x) = 5x - 2 + 2x + 1
LIKE TERMS are terms having same variable with same degree.
Simplify by adding like terms, we have,
f(x) + g(x) = 5x + 2x - 2 + 1
f(x) + g(x) = 7x - 1
Thus, (f + g)(x) = 7x - 1
Given a set of data, what steps would you take to identify whether the data showed linear or exponential growth?
Answers
Answer:
See explanation
Step-by-step explanation:
The first thing to do when given a data set is to ensure that the x-values are spaced in equal intervals.
The next is now to determine if the given y-values are increasing by the same amount(a common difference) or by the same ratio(a common ratio).
The data set is linear if the y-values increase by a common difference and the data set is exponential if the y-values increase by a ratio or factor.
Answer:
Which of the following steps did you include? Check all of the boxes that apply.
Make sure that the x-values are spaced apart in equal intervals.
Determine whether the y-values increase by the same amount or by the same ratio.
Decide that the data is linear because the y-values increase by a common difference.
Decide that the data is exponential because the y-values increase by a ratio or factor.
Step-by-step explanation:
i took the test
A carpenter designs a tabletop in the shape of an ellipse 7 feet long and 4 feet wide. The carpenter sketches a drawing of the tabletop on a coordinate plane. The center of the tabletop is at the origin, the length falls along the x-axis, and the width falls along the y-axis. Which equation represents the tabletop?
Answers
Answer:
C
Step-by-step explanation:
x^2/12.25 + y^2/4 = 1
A carpenter designs a tabletop in the shape of an ellipse 7 feet long and 4 feet wide then, the equation of that ellipse would be [tex]\dfrac{ x^2}{12.25} + \dfrac{ y^2}{4} = 1[/tex]
What is the equation of ellipse if its major and minor axis and center are given?Suppose that the major axis is of the length 2a units, and that minor axis is of 2b units, and let the ellipse is centered on (h,k) with a major ellipse parallel to x-axis, then the equation of that ellipse would be:
[tex]\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2} =1[/tex]
Coordinates of its foci would be: [tex](h \pm c, k)[/tex] where [tex]c^2 = a^2 - b^2[/tex]
If its major axis is parallel to y-axis, then,
Coordinates of its foci would be: [tex](h , k\pm c)[/tex] where [tex]c^2 = a^2 - b^2[/tex]and its equation would be:
[tex]\dfrac{(x-h)^2}{b^2} + \dfrac{(y-k)^2}{a^2} =1[/tex]
A carpenter designs a tabletop in the shape of an ellipse 7 feet long and 4 feet wide.
The carpenter sketches a drawing of the tabletop on a coordinate plane.
The center of the tabletop is at the origin, the length falls along the x-axis, and the width falls along the y-axis.
then, the equation of that ellipse would be:
[tex]\dfrac{ x^2}{12.25} + \dfrac{ y^2}{4} = 1[/tex]
Learn more about ellipse here:
https://brainly.com/question/19881832
#SPJ2
a pencil costs 16p and a rubber costs 23p. bob purchases 18 pencils and 12 rubbers. Calculate how much he spends
Answers
Answer:
564p
Step-by-step explanation:
I hope this helps you.
Please help!
Select ALL of the expressions that are equivalent to
3.5 – (4.7).
3.5+ (-4.7)
4.7 – (3.5)
-4.7 + 3.5
3.5 +4.7
3.5 - (-4.7)
Answers
Answer:
Step-by-step 16
16 x 81
Please help me. Thank you!
Answers
Answer:
25
Step-by-step explanation:
I don't know the steps
PLZ HELP! I'M ON A TIME CRUNCH!
Diego scored 9 points less than Andre in the basketball game. Noah scored twice as many points as Diego. If Noah scored 10 pints, how many points did Andre score?
Answers
Answer:
Let andre score be x points.
then Diego's score will be (x-9) points.
Noah's points=2(x-9) points
the equation is 2(x-9) = 10
dividing both sides by 2,
2(x-9)/2 =. 10/2
x-9= 5
adding 9 both sides,
x-9+9= 5+9
x=14.
Step-by-step explanation:
Answer:
Andre score 14 points
Step-by-step explanation:
noah = 2*diego
diego = andre - 9
given noah = 10
noah = 2*Diego
10 = 2*Diego
Diego = 5
diego = andre - 9
5 = andre - 9
andre = 9 + 5
Andre = 14
11 is what percentage of 16? Round the nearest tenth.
Answers
Answer:
.69, but you can round it to .70 because of the 9
Step-by-step explanation:
70%
Answer:
This can be calculated by dividing 11 over 16, which is equal to about 0.69.
Let me know if this helps!
Complete the equations so that the solution of the system of equations is (−1, −4). y= ?X−11 6x− ? Y=10
Answers
Answer:
y = –7x – 11
6x – 4y = 10
Step-by-step explanation:
From the question given above, we obtained:
x = –1
y = –4
y = ?x – 11 ....... (1)
6x – ?y = 10b......... (2)
Let the two unknown be a and b. Thus the above equation becomes:
y = ax – 11 ......... (3)
6x – by = 10 .......(4)
Next, we shall determine the value of 'a' and 'b'. This can be obtained as follow:
For a:
y = ax – 11
x = –1
y = –4
–4 = a(–1) – 11
–4 = –a – 11
Collect like terms
–4 + 11 = –a
7 = –a
Multiply through by –1
a = –7
For b:
6x – by = 10
x = –1
y = –4
6(–1) – b(–4) = 10
–6 + 4b = 10
Collect like terms
4b = 10 + 6
4b = 16
Divide both side by 4
b = 16 / 4
b = 4
Finally, we shall substitute the value of a and be into equation 3 and 4 respectively.
y = ax – 11
a = –7
y = –7x – 11
6x – by = 10
b = 4
6x – 4y = 10
Therefore, the complete equation are:
y = –7x – 11
6x – 4y = 10
Order -5,-7,0, and 4 from least to greatest
Answers
Answer:
-7,-5,0 and 4 is from the least to the greatest.
Answer:
-5,-7,0,4
Step-by-step explanation:
-5
-7
0
4
9(3+v)
answer pleaseee
Answers
Answer:
27+9v
Step-by-step explanation:
distribute
It’s distributing. You multiply 9 with 3 and v. And the answer will be :
= 27+9v
An average person can type 2,4002,400 words per hour. Trista types at the same rate as the average person and made the double number line below to estimate how long it will take her to type her research paper. Using Trista's double number line, estimate how long it will take her to type her 1,400-word research paper.
Answers
Answer:
35 minutes
Step-by-step explanation:
Given that:
Trista:
Average word type per hour = 2400 words /hr
For Trista to type her 1400 word research paper ;
It will take 'h' hour
If
2400 words = 1 hour
1400 words = h
Cross multiply :
2400h = 1400
h = 1400 / 2400
h = 0.5833333 hr
To minutes, it will take :
0.5833333 * 60 = 35 minutes
Hence, it will take Trista 35 minutes or 0.5833333 to type her 1400 words research paper.
The puppy weighed 2 pounds when it was born. He has gained weight, but still weighs less than 11 pounds. How much weight could he have gained?
Answers
because it has to be more than 2 pounds and less than 11. hope it helps
Volume of cylinder & cone ... Help me please
Answers
Answer:
The formula for the volume of a sphere is 4⁄3πr³. For a cylinder, the formula is πr²h. A cone is ⅓ the volume of a cylinder, or 1⁄3πr²h.
Estimate 13.5 km to miles ASAP!!!
Answers
Answer:
8.388511
Step-by-step explanation:
Divide by 1.609
2 Which of the following fractions are equivalent to 2/4?
Answers
Answer:
1/2=2/4
Step-by-step explanation:
Kenny wants to take his dog to obedience school. At Sit and Stay School, 12 lessons cost $96. At Canine Community Center, 25 lessons cost $125. Which is the better deal?
Answers
Answer:
25 lessons that cost $125
Step-by-step explanation:
If 8 lessons cost $96
then, 96/12 =8
therefore a lesson costs $8
If 25 lessons costs $125
then, 125/25= 5
therefore a lesson costs $5 which is cheaper.
THIS IS WORTH 100 POINTS IF YOU’RE CORRECT!!! I WILL GIVE BRIANLIEST!!!!!!!!
Please, I really need to get these right because I’m redoing it for full credit and I have an F in math, help me with as many as you can but don’t guess because I really need this. Even if you see other people’s answers, please give me your feedback still.
Answers
Answer:
The Correct Answer Is D
Step-by-step explanation:
I hope it Helps!
Kathy wants to paint the faces of her standard six-sided die so that each face is either red or blue. However, she does not want all of the faces to be the same color. How many ways are there for Kathy to paint her die?
Answers
Answer:
The number of ways Kathy can paint her die is 52 ways
Step-by-step explanation:
The permutation and combination related question is answered as follows;
The number of faces in the six-sided die = 6
The number of colors available for painting the six-sided die = 2 colors
Therefore, we have, the total number of ways Kathy can paint her die, 'n', given as follows;
n = ₆P₂ + 2₄P₄ + 2₄P₃ + ₄P₂
Where;
₆P₂ = The number of ways of arranging 2 objects in 6 spaces = 30
₄P₄ = The number of ways of arranging 4 objects in 4 spaces = 1
₄P₃ = The number of ways of arranging 3 objects in 4 spaces = 4
₄P₂ = The number of ways of arranging 2 objects in 4 spaces = 12
∴ n = 30 + 2×1 + 2×4 + 12 = 52
The number of ways Kathy can paint her die, n = 52 ways.
The diameter of a circle is 40.0cm. What is the circumference of the circle?
Use 3.14 for pi
Help would really be appreciated bc I do not understand circles lol
Answers
Answer:
Answer is 125.6
Step-by-step explanation:
Diameter=40cm
radius=40÷2 = 20cm
Circumference = 2πr
=2×3.14×20
=125.6
solve using a2 + b2 = c2
show the work please :)
Answers
Answer: 19.20937
Step-by-step explanation:
a2=15
b2=12
c2=?
a2+b2=c2
15(15)+12(12)= c2
225+ 144=c2
√369= √c2
≐19.20937 ft
3√41
hola please help i’ll give brainliest but please answer correctly
Answers
Answer:
Step-by-step explanation: 1) 14.5 bc
We have the equation:
43.5 ÷ 3 = 14.500
Calculated to 3 decimal places.
2) They are all the same because they are the same numbers but in different places.
i hope this helps! =3
help pls brainliest for whoever helps me ·ω·
Answers
Answer:
8
Step-by-step explanation:
Answer:
Answer is 8 :D
Step-by-step explanation:
The common factor of those 2 numbers are 1, 2,4,8 :)
Find the value of x.
A. 4.3
B. 2.7
C. 11.6
D. 13.9
Answers
Answer:
[D] 13.9Explanation:
Pythagorean theorem: a² + b² = c²Solve for hypotenuse (side x) using: c = √a² + b²12.8² + 5.3² = 191.93
√191.93
= 13.8538803229
Round the answer
13.9
PLEASE PLEASE HELP THE OTHER BRAINLY ANSWERS WERE WRONG IM BEING TIMED
A _____ organizes lots of information into tidy categories, but does not necessarily show a clear relationship among them.
pie chart
pictograph
table
line graph
bar graph
Answers
Answer:
A table?
Step-by-step explanation:
fingers crossed this is right
Roman and Ranjan each divided 3.56 by 0.72. Roman got 4.94 for his quotient. Ranjan got 0.04 for his quotient. Which student divided correctly? How do you know? P 7•3
Answers
Answer:
Step-by-step explanation:
It’s Roman if you do the math you will get 4.94
How would you know
When doing the math i got the answer 4.94 which that mean ranjan divide wrong
An alarm rings 8 times in 5 seconds. What is the unit rate ,in rings per second?
Answers
‼️please help ASAP.
Answers
Let u= <-6,3>, v=<1,9>. Find u-v
Answers
Answer:
??????????????
Step-by-step explanation:
Ummm is that a equation??? If so ill try.....
(-6,3)-(1,9)= (-8,2)
(-6,3)+(1,9)= (-4,4)
find the area of the circle with a cirumfererference of 30pi write your solution in terms of pi
Answers
Answer:
225 pi
Step-by-step explanation:
2pi r=30pi
pi r =15pi
pi r2=225pi
225 pi
