Which statements are true about the graph of the function f(x) = x2 – 8x + 5? Select three options.
The function in vertex form is f(x) = (x – 4)2 – 11.
The vertex of the function is (–8, 5).
The axis of symmetry is x = 5.
The y-intercept of the function is (0, 5).
The function crosses the x-axis twice.
Answers
the y-intercept of the function is (0,5)
the function crosses the x-axis twice
The equation is f(x) = x² – 8x + 5. Then the y-intercept is at (0, 5) and the function crosses the x-axis twice. Then the correct options are A, D, and E.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The quadratic equation is given below.
f(x) = x² – 8x + 5
Convert the equation into vertex form, then the equation will be
f(x) = x² – 8x + 5
f(x) = x² – 8x + 16 – 16 + 5
f(x) = (x – 4)² – 16 + 5
f(x) = (x – 4)² – 11
The graph of the function is given below.
From the graph, the y-intercept is at (0, 5) and the function crosses the x-axis twice.
Then the correct options are A, D, and E.
More about the equation of parabola link is given below.
https://brainly.com/question/20333425
#SPJ6
Related Questions
What is the volume of the cylinder when the radius is 10 and the height is 15
Answers
v=pi*10^2*15
v=4712.39u^3
Answer:
V = π r^2 h = π · 10^2 · 15 ≈ 4712.38898
Jonathan has 25 coins in his pockets and they are all either nickels or quarters. If he has a total of
$3.25, how many of the coins are nickels and how many are quarters. Give me two equations and the answer in nickels and quarters
Answers
Answer:
The answer is 10 quarters and 15 nickels
Step-by-step explanation:
Lets say x equals the number of quarters and y quals the number of nickels. Since there is a total of 25 coins that means that x+y=25. But, the quarter costs 0.25, and the nickel costs 0.05. That means that we have to multiply the number of each coin with their cost. Which leads us to: (x*0.25)+(y*0.05)=3.25. By solving these two equations you'll see that x=10 and y=15.
Given the diagram below, which statements are true? Check all that apply. *
<1 and <4 are vertical and congruent angles.
<1 and <5 are adjacent and complementary angles.
<2 and <4 are vertical and complementary angles.
<4 and <5 are adjacent and supplementary angles. PLEASE HELP!! Thank you.
Answers
Answer:
<1 and <5
are adjacent and complementary angles
Step-by-step explanation:
hope I'm I'm right tell me if I'm wrong
malayalam note class 8 chapter 1
Answers
have a nice day :]
Answer:
pt2 hope it helps
Step-by-step explanation:
Patrick rosses a penny and a number cube, with faces numbered 1 through 6, at the
same time,
A. Are the events dependent or independent Explain your thinking,
Answers
The events are independent because the outcome of one does not affect the outcome of the other one.
pls help me ill give u candy
Answers
Answer:
8.9
Step-by-step explanation:
8^2+ s^2=12^2
64+s^2=144
s^2=80
s=square root of 80
s=8.9
Calculate the surface area of the figure:
54ft
198ft
21ft
108ft
Answers
Answer:
108
Step-by-step explanation:
An engineer needs to determine the distance across a river without swimming to the other side. The engineer notices a tree on the other side of the river and suddenly has an idea.
Describe how she will sketch her idea to be able to determine the distance. Make a sketch and support you figure by number use meter as unit.
Answers
Answer:
Step-by-step explanation:
The engineer can use a clinometer to measure the angle of elevation of the top of the tree. Let the height of the tree be represented by x, the she could determine the distance across the river, d, by applying the trigonometric function.
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
= [tex]\frac{x}{d}[/tex]
the the distance, d = x ÷ Tan θ
Assume the angle of elevation of the top of the tree is [tex]30^{o}[/tex], and the height of the tree is 10 m, then the distance, d, across the river would be;
d = [tex]\frac{10}{0.5774}[/tex]
= 17.3190
d = 17.32 m
The sketch to the explanation is attached to this answer for more clarification.
Carrie often asks friends to play Among Us at lunch. Of the 5 games they play, Carrie wins 2 games. Consider this data:
If she keeps playing in 35 games, how many games should you expect Carrie not to win
Answers
Answer:
She'll lose 21 games out of 35. But she'll win 14 lol
All I did was see how many fives go into 35, and that's 7. So 3 (how many games she loses per 5 games) times 7 is 21.
Can I get help with this
Answers
Answer:
The correct option is;
B) -6
Step-by-step explanation:
The given parameters are;
The line of symmetry of f(x) = The line of the reflection of g(x) over the y-axis
f(x) = 3·x² + b·x + c
From the given graph of g(x), we have;
The vertex point of g(x) = (-1, 8)
The line of symmetry is the line x = -1
The image of the reflection of (x, y) over the y-axis is (-x, y)
The image of the vertex of g(x) following a reflection across the y-axis is (1, 8)
Therefore;
The line of symmetry of the image of g(x) following a reflection over the x-axis is the line x = 1
The line (axis) of symmetry of a quadratic function is the line x = -b/(2·a), which is a line that always go through the vertex of the parabola
Where;
a = The coefficient of x²
b = The coefficient of 'x'
For f(x) = 3·x² + b·x + c, a = 3, and b = b
Given that f(x) and the image of g(x) have the same line of symmetry, we have;
The line of symmetry of f(x) is x = 1
Therefore, from the formula for the line of symmetry, we have;
x = -b/(2·a)
x = 1
By substitution, we have;
1 = -b/(2·a)
∴ -2·a = b
Given that a = 3, we get;
-2 × 3 = -6 = b
b = -6
a mug in the shape of a cylinder has a base of with a radius of 4 cm. how many milliliters of liquid does it hold if filled to a height of 9cm?
(1 cm3 holds 1mL)
Answers
Answer:
v= 452.2 cm^3 or 452.2 mL
Step-by-step explanation:
v= pi(r)^2h
v=pi(4)^2(9)
v=452.2 cm^3
15. Andre manages a company that currently has 35 employees and is gaining 4 new employees
each month. Write an equation to represent the relationship between y, the total number of
employees, and x, the number of months it has been.
Answers
PLEASE HELP I DONT UNDERSTAND!!! Mason works in a cell phone store where he earns a base salary of $105 per a day plus 15% of his sales. He earned $600 by working on a Saturday and Sunday and sold the same amount on both days. Select all of the statements that help explain how to find his sales for each day.
A. Mason's base salary is $105, so over the 2 days he earned $210.
B. Subtract $210 from $600 to find he made $390 on sales.
C. Mason's base salary is $600, so over the two days he earned $1,200.
D. Multiply $390 by 0.15 to find he sold $58.50 worth of cell phones. Divide $58.50 by 2 to find he sold $29.25 worth of cell phones each day.
E. Divide $390 by 0.15 to find he sold $2,600 worth of phones. Divide $2,600 by 2 to find he sold $1,300 worth of phones each day.
F. Add $1,200 to $105 to find Mason made $1,305 on phone sales.
Answers
Answer:
I think b, sorry im not as good
Which are examples of unit rates? Check all that apply.
1. $45 per ticket
2. 5 shows every 3 weeks
3. 30 seats for every row
4. $100 for 5 tickets
Answers
PI QUESTION PLEASE HELP DUE TODAY HURRY DON'T GO PAST AND ONLY ANSWER IF YOU KNOW THE ANSWER!!!!! CORRECT ANSWER = BRAINLIEST!!!!!!!!!
Answers
Answer:
Area of Shaded Region; 6.25π square inches
Good luck <3
Answer: 19.625in
Step-by-step explanation:
If a tank leaks 10 mL of fluid each hour, how long will it take to fill up a one-litre jar?
10 hours
1,000 hours
1 hour
100 hours
Answers
Answer:
100 hours
Step-by-step explanation:
To find the amount of liters in one hour, you divide 10 by 1000, which gives 0.01 liters each hour. From here, the 1 is in the hundredths place, so if you multiply by 100 hours, if will be at 1 liter.
Using the exponential growth function for the U. S. population from 1970 through 2003:
A = 205.1e^0.011t
with the U.S. population being 205.1 million in 1970,
when would the U. S. population reach 350 million?
A.
2028
B.
2048
C.
2018
D.
2038
Answers
Answer:
Step-by-step explanation:
Using the exponential growth function for the U. S. population from 1970 through 2003:
A = 205.1e^0.011t
with the U.S. population being 205.1 million in 1970, when would the U. S. population reach 350 million?
A.
2028
B.
2048
C.
2018
D.
2038
We have the expression
A = 205.1e^0.011t
We are asked to find when would the U. S. population reach 350 million
A = 350
350 = 205.1e^0.011t
We divide both sides by 205.1
Divide both sides by 205.1
350/205.1 = 205.1e^0.011t/205.1
1.7064846416 = e^0.011t
We take the log of both sides
log 1.7064846416 = log e^0.011t
log 1.7064846416 = t log 0.011
t = log 1.7064846416/ log 0.011
t = 0.1185057826
The diameter of a circle is 75, find the circumference of the circle. Round your answer to
the nearest hundredth. (Two numbers after the decimal point).
Answers
Answer:
C ≈ 236
Step-by-step explanation:
Formula
Using the formulas
C=2πr
d=2r
Solve
Solving for C
C = πd = π· 75 ≈ 235.61945
C ≈ 235.62
To the nearest hundredth.
C ≈ 236
Ethan has partially filled the prism with 8 unit cubes.
A rectangular prism with length, height, and width of 3.
How many more cubes does he need to fill the prism completely?
10
15
19
21
Answers
Answer: is it c?
Step-by-step explanation:
Answer:
I think C is your answer.
Step-by-step explanation:
Find the number of ways you can arrange (a) all of the letters and (b) two is the letters in the word ROCK. a. The number of ways you can arrange all of the letters in the word is __. b. The number of ways you can arrange two of the letters in the word is __.
Answers
Answer:
a) 24
b) 12
Step-by-step explanation:
a) For the 4 letters of the word ROCK
Selecting any first letter, we have 4 options
for the second, we have 3 options
for the third we have 2 options
for the fourth, we have only one option
So the number of ways will be ;
4 * 3 * 2 * 1 = 24 ways
b) 2 out of 4
For the first letter, we have 4 options, for the second, we have 3 options
so the number of options is 4 * 3 = 12 options
Pierre was plotting the quadratic function f(x) = - x ^ 2 + 8x for an exit ticket His work is shown below .
Answers
Answer:
(a) The table
[tex]\begin{array}{cc}x & {f(x)} & {0} & {0} & {1} & {7}& {2} & {12} & {3} & {15} & {4} & {16} & {5} &{15} & {6} & {12} & {7} &{7} & {8} & {0}\ \end{array}[/tex]
(b) See attachment for graph
(c) He swapped the values of the x and y coordinates for one another
Step-by-step explanation:
Given
See attachment for complete question
Solving (a): Complete the table
[tex]f(x) = -x^2 + 8x[/tex]
[tex]x = 0[/tex]: [tex]f(0) = -0^2 + 8*0 = 0 + 0 = 0[/tex]
[tex]x = 1[/tex]: [tex]f(1) = -1^2 + 8*1 = -1 + 9 = 7[/tex]
[tex]x = 2[/tex]: [tex]f(2) = -2^2 + 8 *2 = -4 + 16 = 12[/tex]
[tex]x = 3[/tex]: [tex]f(3) = -3^2 + 8 *3 = -9 + 24 = 15[/tex]
[tex]x = 4[/tex]: [tex]f(4) = -4^2 + 8 *4 = -16 + 32 = 16[/tex]
[tex]x = 5[/tex]: [tex]f(5) = -5^2 + 8 *5 = -25 + 40 = 15[/tex]
[tex]x = 6[/tex]: [tex]f(6) = -6^2 + 8 *6 = -36 + 48 = 12[/tex]
[tex]x= 7[/tex]: [tex]f(7) = -7^2 + 8 *7 = -49 + 56 = 7[/tex]
[tex]x = 8[/tex]: [tex]f(8) = -8^2 + 8 *8 = -64 + 64 = 0[/tex]
So, the complete table is:
[tex]\begin{array}{cc}x & {f(x)} & {0} & {0} & {1} & {7}& {2} & {12} & {3} & {15} & {4} & {16} & {5} &{15} & {6} & {12} & {7} &{7} & {8} & {0}\ \end{array}[/tex]
Solving (b): Plot the graph
See attachment 2 for graph
Solving (c): Why he was marked as incorrect
By comparing the new attached graph (in b) and the graph of the original question, one will notice that the values of the x and y coordinates are switched.
This is why he was marked as incorrect.
what is the value of x? 6x−1=4x−5
Answers
Explanation is I just know the answer
Answer:
x = -2
Step-by-step explanation:
6x - 1 = 4x - 5
Bring like terms together
6x - 4x = 1 - 5
2x = -4
-4 / 2 = -2
Complete the problem
5/10 +8/100
Answers
Answer:
0.58
Step-by-step explanation:
Solve the system of equations 3x = 84 - 2y 9x = 8y - 24
Answers
Answer:
[tex]3x = 84 - 2y - - - (i) \\ 9x = 8y - 24 - - - - (ii) \\ from \: (ii) \\ 3(3x) = 8y - 24 \\ but \: from \: (i) \: \: 3x = 84 - 2y \\ hence \: put \: (i) \: in \: (ii) \\ 3(84 - 2y) = 8y - 24 \\ 252 - 6y = 8y - 24 \\ 276 = 14y \\ y = \frac{138}{7} \\ x = \frac{104}{7} [/tex]
Solve for x and y by using elimination. 4x - 3y = 12 x + 2y = 14
Answers
Answer:
8x + 5y = 14
Step-by-step explanation:
Lance's math quz has eight true faise questions. How many different choices for giving answers to the eight
questions are possible?
Answers
Answer:
2^8 = 256 choices
Step-by-step explanation:
Hiii, I would love it if you can help me with this! I tried my best but it's really hard and I don't understand this.
Answers
Answer:
A
Step-by-step explanation:
82 inches! 6 feet is 72 inches. 12*6
Jamal will cut a piece of wood that is 3 1/2 feet long into 1/4 foot sections. How many sections will result? plz help
Answers
Answer:
14 sections
Step-by-step explanation:
I think I'm correct but if I'm wrong tell me right away I'll try again.
What value(s) for n will make this equation true?
Answers
Answer:
B
Step-by-step explanation:
It the only one that make sense
The data modeled by the box plots represent the battery life of two different brands of batteries that Mary tested. (a) What is the median value of each data set? (b) Compare the median values of the data sets. What does this comparison tell you in terms of the situation the data represent? For 100 point pls
Answers
Answer:
a brand x = 13 (median ) brand y = 16 median
Answer:
A) Median value is depicted on a box plot by the vertical line that divides the rectangular box. Therefore: Median value for Brand X = 13 and Median value for Brand Y = 16. B) Brand Y has a higher median value (16) than Brand X (13). This implies that brand Y has a battery life that last longer than brand X.
