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:
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Triangles â–łABC and â–łDFG are similar. The lengths of the two corresponding sides are 1. 4m , and 56 cm. What is the ratio of the perimeters of these triangles ?.
Answer:
5 : 2
Step-by-step explanation:
The ratio of perimeters of similar triangles is the same as the ratio of any pair of corresponding sides. That ratio is given as ...
1.4 m : 56 cm = 140 cm : 56 cm = 5 : 2
The ratio of the perimeters of the triangles is 5 : 2.
_____
As a unit ratio, it is 2.5 : 1, or 2.5.
Answer I need help plsssssssssssssss??
Answer:
1. -1/2
2. Graph attached below:
Step-by-step explanation:
1) To find to slope of the line with two points would be the following equation:
[tex]y_{2} - y_{1} / x_{2} - x_{1}[/tex]
So let’s assume our variables and subsitute them to see that the Carma’s Working out is an error.
Form: [tex](x_{2}, y_{2}), (x_{1}, y_{1})[/tex]
[tex]y_{2} = 3[/tex]
[tex]y_{1} = 1[/tex]
[tex]x_{2} = 7[/tex]
[tex]x_{1} = 11[/tex]
[tex]3 - 1 / 7 - 11 = -1/2[/tex]
1. Error one: The point values of the slope aren‘t correctly labeled and are not the same form as in the formula.
2. Error two: The slope output is not correct, it is 2 but the slope is -1/2.
Now let’s get on the graph of Carma’s workout, I can spot that the point (-4, 5) is not plotted correctly. Instead it is plotted (4, -5). To understand clearly I will label these points on a graph, image attached below:
3. Error three: The point (-4, 5) is not plotted correctly, x should be negative and y should be positive.
4. Error four: The slope is not correct, instead the slope of the graph is negative but we need a positive slope.
Now it is time to fix Carma’s mistakes:
1) Slope: -1/2
2) Graph attached below
I need help with this
Answer:
If the bottom is 14 it's 6 and 8
please help asap
ty :)
Answer:
y = 3x + 6
Step-by-step explanation:
Since the line is parallel, it has the same slope -- 3
y = 3x + b, sub point (1, 9)
9 = 3(1) + b
9 = 3 + b
b = 9 - 3
b = 6
y = 3x + b -- y = 3x + 6
Whats the answer? i need help
Answer:
x = 2 and x + y = -3
Step-by-step explanation:
With the xy example filled, I could work out that x was 2 by realising that if y was -5, then to get to -10 it'd have to be multiplied by two, and I just added -5 and 2 after working out x for the bottom grid.
Hope this helps and you have a good day!
Left box is two (2) and the bottom box is negative three (-3)...
...You are given y, which is -5. We need to figure out x to fill the other 3
boxes or diamonds. xy is another way of saying x * y, so we know that
x * -5 = -10. We can use division to solve this. -10 / -5 = x, or 2. Now we can
fill in the top and left diamond. All that's left is to add x and y, or 2 and -5
together.
2 + -5 = -3
Top diamond : -10
Left diamond : 2
Bottom diamond : -3
Right diamond : -5
Hopefully this helps.
2x+5y>−6
−4x+3y≤2
Is (-1,7)(−1,7)left parenthesis, minus, 1, comma, 7, right parenthesis a solution of the system?
Answer:
No
Step-by-step explanation:
Khan told me ;p
Answer:
No
Step-by-step explanation:
What is the y-intercept of the graph of the function f(x) = x2 3x 5?.
Answer:
f(x) =x2 3x 5?
c = 5
therefore the solpe = 5
The statue of liberty casts a 122 foot shadow at the same time ryan casts a 2 foot shadow. If the statue of liberty is 305 feet tall how tall is ryan?
Step-by-step explanation:
2 objects and their shadows create 2 similar right-angled triangles.
that means all angles are the same, and the side lengths of one triangle correlate to the corresponding side lengths of the other triangle via the same factor.
so,
122 × f = 2
f = 2/122 = 1/61
therefore, Ryan is
305 × f = 305 × 1/61 = 5 ft
tall.
If the Statue of Liberty is 305 feet tall, Ryan is 5 feet tall.
What is proportion?A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio.
Given that,
The length of shadow of Statue of Liberty = 122 foot.
The length of shadow of Ryan = 2 foot.
Also, the height of Statue of Liberty = 305 feet.
Let the height of Ryan = x
To find the value of x,
Use ratio and proportion method,
122 / 305 = 2 / x
x = 2 x 305 / 122
x = 305 / 61
x = 5
The height of Ryan is 5 feet.
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could some one answer this
Answer:
12
Step-by-step explanation:
So she went there 4 times. Each time, she pays for the salad itself (we don't know how much) and she also leaves a 1,50 dollar tip. All together, she paid 54 dollars.
-> TIPS: 4x 1,50= 6 (dollars)
-> SALADS: 54 (total amount she paid) - 6 (tips) = 48 (all the 4 salads she bourght)
-> 1 SALAD: 48/4=12
-----------linear equation:-------------
54 = 4 x 1,5 + 4 x c
54 = 6 + 4c
48 = 4c
12 = c
3\sqrt{ }528
please help
Answer:
8.08248
Step-by-step explanation:
Use a calculator
Unit 1C Quiz
3 of 83 of 8 Items
Question
An Uber driver charges a flat fee of $5.50, plus $1.50 per mile. Which of the following equations represents the total cost y of a ride that is x miles long.
a. y=1.5+5.5
b. y=4x
c. y=5.5x +1.5
d. y=7x
Answer:
y = 1.5x + 5.5
Step-by-step explanation:
None of them are correct. The correct answer, y = 1.5x + 5.5, is not listed.
how many times longeris the perimeter of the shorter side?
Answer: Which shape are you talking about?
Find the perimeter and area of a rectangle with the sides 3 3/10 meters and 6 2/3 meters
QUICKK
pls say area AND perimeter
PLZZZ HELP
Order these numbers from least to greatest.
Answer:
51/10, 4 and 1/9, 5.116, and 5.98
Step-by-step explanation:
least to greatest
Answer:
4 1/9, 51/10, 5.116, 5.98
Step-by-step explanation:
4 1/9
= 37/9
= 4.111...
51/10
= 5.1
I really really really need help with this
Answer:
404Step-by-step explanation:
PEMDAS48 ÷ 6 + (5×6) × 13 + 6 = → Parenthesis48 ÷ 6 + 30 × 13 + 6 = → Multiplication, division8 + 390 + 6 = → Addition404[tex]\huge \bf༆ Answer ༄[/tex]
Use PEDMAS/BODMAS rule for simplification !
Let's solve ~
[tex] \sf{48} \div 6 + (5 \times 6) \times 13 + 6[/tex][tex] \sf48 \div 6 + 30 \times 13 + 6[/tex][tex] \sf8 + 30 \times 13 + 6[/tex][tex] \sf8 + 390 + 6[/tex][tex] \sf404[/tex]Write a function for the line with a slope of 5 that passes through the point (2, 1). Enter the correct equation in the box.
Answer:
brainly
Step-by-step explanation:
By which rule are these triangles congruent?
АА
SAS
SSA
AAS
Answer:
it's AAS is my opinion
Step-by-step explanation:
Answer:
AAS
Step-by-step explanation:
we can eliminate two of the answer choices from the start. AA and SSA do not prove triangle congruence. we are then left with SAS and AAS. we can see that there is one pair of sides and one pair of angles marked congruent on the triangles. the triangles are formed by intersecting lines which form vertical angles. according to the vertical angles theorem, those two angles will be congruent. therefore, these triangles are proven congruent by AAS. hope this helps!
What is the least angle measure by which this figure can be
rotated so that it maps onto itself?
O 45°
O 90 °
O 180°
O 360°
Answer:
Step-by-step explanation:
360° degrees
The least angle measure by which this figure can be rotated so that it maps onto itself is 360 degrees option (D) 360° is correct.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
It is given that:
The two-dimensional figure is shown in the picture.
As we know from the definition of the geometric transformation; the change in coordinates and the shape of the geometrical body and geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
The least angle measure by which this figure can be rotated so that it maps onto itself is 360 degrees
Because the rotation of 45, 90, and 180 degrees cannot map the figure onto itself.
Thus, the least angle measure by which this figure can be rotated so that it maps onto itself is 360 degrees option (D) 360° is correct.
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Im just straight up confused. And dont leave a link
Answer:
The bottom left graph is a function
Step-by-step explanation:
I was pretty confused at first with this, too. To find if a graph is a function, however, just preform the vertical line test! Basically, draw a vertical line on each graph. At any point does it go through two or more points? Well, its not a function. We can see a vertical line would completly overlap the first graph, it would go through the half circle graph twice, and the circle? Well, that ones rather obvious...
With this test, we can see the only graph that passes the vertical line test is the bottom left graph (or the weird squiggly one)!
Hope this helps for future function solving!
Write an equation of the line that passes through (7,10) and is perpendicular to the line y=1/2x−9.
y = -2x + 24
hope this is helpful!
Answer:
y+2x=24
Step-by-step explanation:
the equation of the line: y=1/2x -9
Get the slope by using derivative:
dy/dx= 1/2
dy/dx= slope of the normal line
Since we are looking for slope of the tangent line:
Use Mn=-1/Mt
The slope of the tangent line is -2
Using point slope form:
(y-y1)=m(x-x1) ; where x1=7, y1=10, and m=-2
y-10=-2(x-7)
y-10=-2x+14
ANSWER: y+2x=24
What is meant by a stratified sample?
Answer:
A stratified random sampling involves dividing the entire population into homogeneous groups called strata (plural for stratum). Random samples are then selected from each stratum. ... A random sample from each stratum is taken in a number proportional to the stratum's size when compared to the population.
Answer:
Sampling that is used to represent different groups depending on their different qualities.
Hope that helps. x
A supervisor finds the mean number of miles that the employees in a department live from work. He finds x Overbar = 29 and s = 3. 6. Which mileage is within a z-score of 1. 5? 21 miles 24 miles 36 miles 41 miles.
The correct option is (B).24 miles.
Z-score is basically another term for the specific number of standard deviations. I suppose we can assume normality here, even though it isn't given, so I'd make a rough sketch.
Otherwise, just use the basic formula:
[tex]z_{score} =\dfrac{x-\mu}{\sigma}[/tex]
Given that,
[tex]\bar{x}=29[/tex] (statistic for a mean) and [tex]s=3.6[/tex] (statistic for a standard deviation).
Since z-score must be Less than 1.5, So
[tex]1.5> \dfrac{x-29}{3.6}\\[/tex]
[tex]1.5 \times3.6 > x-29\\5.4+29> x\\34.4> x[/tex]
I just used normal cdf and got [tex]23.6<x<34.4[/tex].
Hence the correct option is (B).24 miles.
For more details on z score follow the link:
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Answer:
B
Step-by-step explanation:
Correcct on edge22
How i can answer this question
Answer:
A
Step-by-step explanation:
They both equal 2(x+y+1)
Which of the following values could represent the probabilities of complementary events? StartFraction 1 over 7 EndFraction and StartFraction 2 over 7 EndFraction 28% and 82% Two-fifths and Three-fifths 10% and 80%
Answer:
a
Step-by-step explanation:
Answer:
2/5 and 3/5
Step-by-step explanation:
PLEASE HELP ME!!!!!!!
Answer:
The answer is B
Step-by-step explanation:
The answer would be B because the domain of a function is always all real numbers.
Simplify (2x-1/x^2-2x-3) + (1/x-3)
Please provide a step by step
Answer:
(3x - 9)/(x² - 5x + 12)
Step-by-step explanation:
Answer attached, please refer it.
Hope it helps :)
Complete the process of solving the equation.
Fill in all missing terms and select all missing descriptions. Simplify
any fractions.
15c + 11 + 6 = 17
15c + 17 = 17 (A : add 11 to both sides.
B : subtract 11 from both
sides.
C: multiply both sides
By 11.
D: divide both sides by
11.
E: combine like terms.
15c = ?
c = ?
Answer:
I can't understand what to do, so I hope this helps
15c=0
c=0/15 or c=0
Step-by-step explanation:
15c + 11 + 6 = 17
subtract 11 from both sides
15c + 6 = 6
subtract 6 from both sides
15c=0
divide both sides by 15
c=0/15
WILL REWARD BRAINLIEST!!! plz :,) this is my last question:(( 50 POINTS!!!! Hellppp me with this!!!! Click to view whole pics!!! If you can view it it basically says : You are making several purchases from the B-Better Electronics store. You can buy from this store online or in a physical store. You have a coupon for 20% off that can only be used in the physical store and a $20.00 off coupon that can only be used online. The sales tax of 7.5% only applies to the physical store.
Shipping for the online store is a flat rate of $8.99 or free for purchases over $75.00. Using the information below, which way of purchasing would save you the most money?
B-better electrics store:
Headphones. 1 pair. 14.99/e
DVDs 4dvds 13.95/e
CDs. 2cds. 9.85/e
————————————————-
Online store:
Headphones 1 pair. 13.50/e
DVDs. 4dvds 14.99/e
CDs. 2cds. 10.99/e
————————————————-
Answer:
77.82 $ will be paid at physical Store
Step-by-step explanation:
Item Quantity Physical Store Online Store
Headphones 1 pair $14.99/ea $13.50/ea
DVDs 4 DVDs $13.95/ea $14.99/ea
CDs 2 CDs $9.85/ea $10.99/ea
Cost Price = 14.99 + 4 * 13.95 + 2 * 9.85
= 90.49 $
20% off Coupon = (20/100)90.49 = 18.1 $
Amount after Coupon = 72.39 $
7.5% sales Tax = (7.5/100)72.39 = 5.43$
Amount with Tax = 72.39 + 5.43 = 77.82 $
77.82 $ will be paid at physical Store
Answer:
Step-by-step explanation:
i want points thanks
Find the surface area of the cuboid.
Answer:
62 cm²
Step-by-step explanation:
The surface area (SA) is the sum of the areas of the 6 faces.
The opposite faces are congruent, then
SA = area of front/ back + area of top/ bottom + area of 2 sides
= 2(5 × 3) + 2(5 × 2) + 2(3 × 2)
= 2(15) + 2(10) + 2(6)
= 30 + 20 + 12
= 62 cm²
Name all points collinear with point E.
Answer:
n,c,b
Step-by-step explanation: