The shape of the graph of quadratic functions is the shape of a parabola.
The steps for drawing a graph of the function f(x) = 2·(x + 4)² - 3 arranged in the correct order are;
(a) Plot the vertex (-4, -3)(b) Apply the 2·x² pattern, from the vertex go right 1 up 2 and plot (-3, -1)(c) Apply the 2·x² pattern again, from the vertex go right 2 up 8 and plot (-2, 5)(d) Apply the 2·x² pattern a 3rd time, from the vertex go right 3 up 18 and plot (-1, 15)(e) Draw the axis of symmetry x = -4(f) Reflect the points over the axis of symmetry and plot (-5, -1), (-6, 5), and (-7, 15)(g) Draw a U shaped parabola.Reasons:
The given function is; f(x) = 2·(x + 4)² - 3
The function is given in the vertex form; f(x) = a·(x - h)² + k
Therefore, the vertex, (h, k) = (-4, -3)
Step (a);
The vertex can be plotted on the graph
Plot the vertex (-4, -3)Step (b);
Given that the quadratic term is 2·x², the pattern that can be used for the points from the vertex is therefore, 2·x²
From the vertex (-4, -3) apply the 2·x² pattern by going to the right 1 unit and up 2 × 1² = 2 units to get the point (-4 + 1, -3 + 2) = (-3. -1)
Apply the 2·x² pattern, from the vertex go right 1 up 2 and plot (-3, -1)Step (c);
To get the next point, the 2·x² pattern is applied with x = 2, to the vertex to get; (-4 + 2, -3 + (2×2²)) = (-2, 5)
Apply the 2·x² pattern again, from the vertex go right 2 up 8 and plot (-2, 5)Step (d);
A third point on the graph relative to the vertex is obtained again by applying the 2·x² pattern again to the vertex with x = 3, to get;
(-4 + 3, -3 + (2 × 3²)) = (-1, 15)
Apply the 2·x² pattern a 3rd time, from the vertex go right 3 up 18 and plot (-1, 15)Step (e);
The axis of symmetry can be drawn with a vertical line passing through the vertex, which is the line, x = -4
The line x = -4 can be drawn on the graph next
Draw the axis of symmetry x = -4Step (f);
The points obtained relative to the vertex (-3, -1), (-2, 5), (-1, 15) can reflected about the axis of symmetry x = -4, to get;
(-3, -1) [tex]\underrightarrow {R_{(x = -4)}}[/tex] (-5, -1)
(-2, 5) [tex]\underrightarrow {R_{(x = -4)}}[/tex] (-7, 5)
(-1, 15) [tex]\underrightarrow {R_{(x = -4)}}[/tex] (-7, 15)
Reflect the points over the axis of symmetry and plot (-5, -1), (-6, 5), and (-7, 15)Step (g);
The parabola that is U shaped can be drawn from the points plotted in the steps above.
Draw a U shaped parabolaLearn more about drawing the graph of a quadratic function here:
https://brainly.com/question/6353430
What is an equation of the line that passes through the points (0, -4) and (-4, 6)?
I got this answer by first using the slope formula, which would result into [tex] \frac{0 - 4}{6 - 0} \\ [/tex]for which the answer would be - ⅔ Then, the y-intercept could be found easily, since you already have it., which is (0,4). Since the format for all linear equations are y=mx+b , in which b means the y-intercept and m means the slope. So then, if you substitute - ⅔ for m and 4 for b , you would get
[tex]y = - \frac{2}{3} x + 4 \\ [/tex]
Last week antione had a begging balance of $90 in his account he wrote 3 checks for $10 each from his checking account , withdrew another $20 and finally made a deposit of $100. Write an expression that shows his final account balance at the end of the week
Answer:
$140
Step-by-step explanation:
90-(3x10)-20+100= 140
He started with $90: (90)
Then he wrote 3 checks of $10 each: -(3x10)
Then he withdrew $20: -20
Finally, he made a deposit of $100: +100
Thus, our equation would be: 90-(3x10)-20+100=
(You might want to simplify this expression; giving you 140)
10. John is mixing paint.He uses black, green and blue in the ratio 6:3: 1. How much of black green and blue paint is needed to make a mixture of paint of 500ml.
The given ratio becomes 6x : 3x : x.
6x = black paint
3x = green paint
x = blue paint
6x + 3x + x = 500
10x = 500
x = 500/10
x = 50
6x = 6(50) = 300
3x = 3(50) = 150
x = 50
Answer:
300 ml of the black paint.
150 ml of the green paint.
50 ml of the blue paint.
The prices of some houses in a neighborhood are shown below: House Price A $120,000 B $130,000 C $140,000 D $150,000 E $1,110,000 Based on the data, should the mean or the median be used to make an inference about the price of the houses in the neighborhood?
Answer:
The mean
Step-by-step explanation:
The mean would allow you to make an average aka the inference about the price of houses whilst if you take the median, you're just taking the middle number from a list of numbers and not the average.
Answer: Median
Step-by-step explanation:
Median, because there is an outlier that affects the mean.
Step-by-step explanation:
The outlier is 1,110,000
As you have learned in the lesson, outliers affect means, meaning that you should not use them.
Hope this helped! ❤
Hannah's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=7.1x+55 where y represents the expected quiz score and x represents hours spent on homework that week. What is the meaning of the yy-value when x=1?
Answer:
Expected score with 1 hour of homework
Step-by-step explanation:
(0, 2), (1,7) create a equation that passes through each pair of points
Answer:
y = 5x + 2
Step-by-step explanation:
Given the equation 5x + 2
Plug in 0
y = 5(0) + 2
y = 2
(0,2)
Given the equation 5x + 2
Plug in 1
y = 5(1) + 2
y = 7
(1,7)
Help please
:Ccccccccccccccccccccccccc
Answer:
1. false
2. true
Step-by-step explanation:
sorry if wrong
I don’t anderstands but i wanna help
if 10 seeds are planted, what is the probability that exactly 3 don't grow?
Answer:
10:7
Step-by-step explanation:
take 10 as it is and it becomes 10
then,10-3 it is because when 3 don't grow it subtracts and becomes 7
What is the solution set for x^2 - 2x - 15 = 0
A. {-5, -3}
B. {5, -3}
C. {3, 5}
D. {-3, 5}
Answer:
B
Step-by-step explanation:
I have done this before
Problem 1: Solution to the system of equations
A line is parallel to the line for the equation: -9y = 2x + 35.
What is the slope of the parallel line?
Answer:
-2/9
Step-by-step explanation:
if the line is parallel it has the same slope.
The equation can be written as y = -2/9x - 35/9
so the slope is -2/9
Given the function g(x) = –11 + 12x + x over 3, evaluate g(4).
g(−3)=2
g(0) = 3g(0)=3
Step-by-step explanation:
Given
The attached graph
Required
Determine
g(-3)g(−3)
g(x) = 3g(x)=3
Since a graph has been provided, the question will be solved graphically;
Solving g(-3)
This implies that;
x = -3
And the interpretation is to solve for the y value when x = -3
From the attached graph;
When x = -3; y = 2
Hence;
g(-3) = 2g(−3)=2
Solving g(x) = 3
This implies that;
y = 3
And the interpretation is to solve for the x value when y = 3
From the attached graph;
When y = 3; x = 0
30 POINTS John opens a savings account and decides to deposit $10 each month. Let x represent the number of
months that he has been saving, and y, represent the total amount of money saved.
7. What is the algebraic equation for John's saving plan?
8. How much money will John have saved in 14 months? In 6 months? Show your work and
explain.
9. In how many months will John have saved $100? $175? Show your work and explain.
10. What is the rate of change?
11. How does knowing the rate of change help you in answering questions in this problem?
12. Use your equation to complete the table representing John's savings:
# of Months Saving Account Balance ($)
0
1
2
3
4
Answer:
7.) y=10x
8.) $140 in 14 months, $60 in 6 months
9.) He will have saved $100 in 10 months and $175 in 17.5 months
10.) The rate of change is 10
11.) Knowing the rate of change helps you in answering this problem because it tells you how much money he saves per month.
12.)
0- $0
1- $10
2-$20
3-$30
4-$40
Step-by-step explanation:
7.) The standard form of a linear equation is y=mx+b
The starting balance is 0 so there is no point to adding b. M is the amount of money he deposits each month so that is 10. You plug in the values and you get y=10x (+0)
8.) y=10(14)
$140
y=10(6)
$60
9.) 100=10x
100/10= 10
10 months
175=10x
175/10=17.5
17.5 months
10.) The rate in change is m so 10.
Hope I explained this in simple enough terms. Have a good day!
Please help me with this
Answer:
it is -16
Step-by-step explanation:
I did the math i know for sure
Helppppppppppp!!!!!!!!!!!
I NEED HELP ASAP
The volume of paint used, V liters, is directly proportional to the area, A square feet, that the paint can cover. 5 liters of paint can cover a wall with an area of 75 square feet.
a) What is the constant of proportionality? Tell how you found it.
b) Write an equation relating V and A.
c) How much paint would be needed to cover an area of 180 square feet? Show your work.
Whoever answers me correctly first will get extra points after this!
Hey! I believe this is the answer you're looking for:
https://brainly.com/question/16663256
Step-by-step explanation:
The volume of paint used, V liters, is directly proportional to the area, A square feet, that the paint can cover.
This is written as:
\begin{gathered}V \propto A\\V=kA,$ where k is the constant of proportionality\end{gathered}
(a)5 liters of paint can cover a wall with an area of 75 square feet.
V=5 liters, A=75 square feet.
Substitution into V=kA
5=75k
k=5/75
\text{Constant of proportionality, k}=\dfrac{1}{15}Constant of proportionality, k=151
(b)Substitution of k=\dfrac{1}{15}k=151 into V=kA
The equation relating V and A is:
V=\frac{1}{15}AV=151A
(c)If A=180 Square feet
Volume of paint needed,
\begin{gathered}V=\frac{1}{15} X 180\\=12$ liters\end{gathered}
549.5 to 1 decimal place
Answer:
It is still 549.5
Step-by-step explanation:
Rounding to 1 decimal place is just rounding by the tenth place
So it is still 549.5
Hope this helps!
Don’t answer just for points please~ I need help and I’m struggling lol
Answer: 50
Step-by-step explanation:
5x + 55 = 2x + 100
5x = 2x + 45
3x = 45
x = 15
y equals angle 2
180 = 5(15) + 55 + y
180 = 75 + 55 + y
180 = 130 + y
50 = y
angle is 50
We know that:
=> m∠2 + 5x + 55 = 180°=> 5x + 55 = 2x + 100Because of 180° angle formula.
First, let's solve for x. Then we will solve m∠2.
=> 5x + 55 = 2x + 100=> 5x - 2x = 100 - 55=> 3x = 45=> x = 15Since we have found x, it is time to find m∠2.
=> 5(15) + 55 + m∠2 = 180=> 75 + 55 + m∠2 = 180=> 130 + m∠2 = 180=> m∠2 = 180 - 130=> m∠2 = 50Conclusion:Therefore, the measure of m∠2 is 50°
Hoped this helped.
[tex]BrainiacUser1357[/tex]
part A :A rocket scientist needs to find the overall thrust of a new rocket design. The rocket has two stages: Stage A and Stage B. Stage A’s thrust is defined by the expression 11.2x + 6.4 and Stage B’s thrust is defined by the expression 7.4x − 2.9.
Part b: An engineer accidentally reads the blueprints incorrectly and installs the Stage B thrusters upside-down. What is the combined thrust of the rocket if Stage A is firing normally, but Stage B is applying reverse (negative) thrust?
Answer:the answer is that if thruster b is going the opposite way it will stay in 1 place as thruster a is firing up to make the rocket fly if thruster b is going the opposite way it will just hover with that being said that's the answer
Step-by-step explanation:
Please help me solve for n
To solve for N, you have to work backwards
1. Take off the absolute sigh
the absolute sign only means that the answer must be positive. So that means N could equal to positive and Negative
2. What is 1x6?
This process is called inverse operation. Where you have division, you have multiplications. The answer is 6.
3. The answer is 6 or negative 6, in the fact that -6 would equal to six in the absolute sign.
I hope this helped! If it's wrong blame me!
A planet has a circular orbit around a star. It is a distance of 65,000,000 km from the centre of the star. It orbits at an average speed of 65,000 km/h. How many Earth days does it take the planet to orbit the star? Give your answer to 2 sf.
Answer:
Step-by-step explanation:
Orbit = 2*pi * r
r = 65000000 km
Orbit = 65000000 * 2 * 3.14
Orbit = 406 200 000 km
d = 406 200 000
s = speed = 65000 km / hr
t = time = d / s
t = 406,000,000 / 65000
t = 6280 hours.
1 day = 24 hours.
t = 6280 / 24 = 261.67 days
A photographer charges $12 for a set of 20 pictures. Each picture cost the same amount. At this rate, how many pictures cost $30?
Answer:
Step-by-step explanation:
20/12 = 1 2/3
30 ÷ 1 2/3
= $18
What type of function is represented in the table? exponential linear quadratic logarithmic
2022 EDGE ASSIGNMENT
Modeling Functions Using Finite Differences
1. C
2. A, E
3. B
4. B, D
5. D
6. A
7. B, F
Challenge elementary school has 800 students. Every Wednesday, 12% of the students stay after school for chess. How many students attend chess club on Wednesday?
Answer:
Its 96 bro :) 96 students
Step-by-step explanation:
Basically yeah, 800 is 100% of the population yeah. So just multiply 800 times 12%. 800 x 12% is 96.
96 = 12% of 800, I hope this helps!
If CD = 6 and the perimeter of ABC is 41, what is the perimeter of ABE?
Answer:
53.
Step-by-step explanation:
DE = CD = 6 ( as triangle ACE is isosceles so AD is the perpendicular bisector of CE.
Therefore CE = 12.
AB + BC + AC = 41 (given perimeter of ABC)
AB + BC + AE + 12 = perimeter of ABE.
But AE = AC ( given), so
AB + BC + AC + 12 = perimeter of ABE
Now we know that AB + BC + AC = 41 , so
41+ 12 = perimeter of ABE.
Help please
I provided screenshots of the problem below.
Answer:
This is the graph of a sine function
The y-intercept of the graph is the function value y=0
The smallest positive x-intercept of the graph is located at x=pi/2
The greatest value of y is y=2
For x between x=-pi and x=pi/2, the function value y=>0
Step-by-step explanation:
The diagram shows a rectangle 15cm long and 13cm wide.It has been split into four smaller rectangles. write the area of each small rectangle on the diagram.
[tex]195 cm^{2}[/tex]
Area of each splited rectangles =[tex] \frac{195cm{}^{2} }{4} [/tex]
=[tex]48.75 {cm}^{2} [/tex]
!! PLEASE MARK ME THE BRAINLIEST!!AND I'M REALLY VERY SORRY IF MY ANSWER IS WRONG24 % of 175 calculate this
Answer:
24/100x175 = 42
Step-by-step explanation:
24/100x175 = 42
help please anybody PLEASE
Answer:
18 dimes
Step-by-step explanation:
Since Leon has ”16 fewer than” it’s a symbol to subtract
34-16=18
Answer:
34-16=18 leon has 18 dimes
Step-by-step explanation:
hope this helps
Please help, question in pic
Answer:
D
Step-by-step explanation:
hard to explain but when you rotate 180, you can imagine that a straight line with the center of rotation as the midpoint can be drawn between the image and preimage. you want a mapped to c and you want d mapped to b. having it rotate 180 with the center of rotation being the center of the parallelogram allows you to make those imaginary lines between a and c and d and b. hope this helps