Use the parabola tool to graph the quadratic function f(x)=x2−12x+27.
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Answers
From the question know that [tex]a=1[/tex] and [tex]b=-12[/tex], so lets replace those values in our vertex formula to find the x-coordinate of our vertex:
[tex]h= \frac{-(-12)}{2(1)} [/tex]
[tex]h= \frac{12}{2} [/tex]
[tex]h=6[/tex]
Now lets replace that value into our original function to find the y-coordinate of our vertex:
[tex]f(6)=6^{2} -12(6)+27[/tex]
[tex]f(6)=36-72+27[/tex]
[tex]f(6)=-9[/tex]
Finally, we have our vertex (6,-9)
Now to graph our function we are going to take advantage of its line of symmetry; if the vertex is (6,-9) the line of symmetry of the parabola is x=6, so if we chose the point (6,0), our second point will have coordinates (3,0) as you can see in the picture.
The vertex of a parabola is the minimum or the maximum point of the parabola
The equation of the parabola is given as:
[tex]f(x) = x^2 + 12x + 27[/tex]The x-coordinate of the vertex is calculated using:
[tex]x = -\frac{b}{2a}[/tex]
So, we have:
[tex]x = -\frac{12}{2 \times 1}[/tex]
[tex]x = -\frac{12}{2}[/tex]
[tex]x = -6[/tex]
Substitute -6 for x in f(x)
[tex]f(-6) = (-6)^2 + 12(-6) + 27[/tex]
[tex]f(-6) =-9[/tex]
So, the vertex of the parabola is (-6,-9)
Let x = 0.
So, we calculate f(0) as follows:
[tex]f(0) = (0)^2 + 12(0) + 27[/tex]
[tex]f(0) = 27[/tex]
This means that f(x) passes through (0,27)
See attachment of the parabola
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Related Questions
A trapezoid has an area of 24 square meters. The length of the bases of the trapezoid are 5 meters and 7 meters. What is the height of the trapezoid?
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A = (b1 +b2)/2*h
24 m^2 = (5 m +7 m)/2 * h
24 m^2 = (6 m) * h
(24 m^2)/(6 m) = h
4 m = h
The height of the trapezoid is 4 meters.
What is the equation of the line in slope-intercept form?
[ fill in the spaces ]
y=___x+___
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NEED HELP FAST PLEASE!! Draw the base plan for the set of stacked cubes, assume the no cubes are hidden from view.
Answers
In the figure, point B is the midpoint of AC. Use the figure to answer the questions.
(a) Jeremy says that ABD is congruent to CBD by the SAS congruence postulate. Do you agree or disagree? Explain.
(b) Suppose it is also known that AD is congruent to CD. Which postulate or theorem can be used to prove that ABD is congruent to CBD? Justify your answer.
Answers
Answer:
A is true
B = SSS OR RHS
Step-by-step explanation:
bcoz both can be applied here
Jeremy's statement that triangle ABD is congruent to triangle CBD by the SAS congruence postulate is incorrect.
If we are also given that AD is congruent to CD, then we can use the SSS congruence postulate to prove that triangle ABD is congruent to triangle CBD.
Answer to part (a)
I disagree with Jeremy's statement that triangle ABD is congruent to triangle CBD by the SAS congruence postulate.
The SAS congruence postulate states that two triangles are congruent if they have two pairs of corresponding sides congruent and the included angle congruent.
In this case, we have two pairs of corresponding sides congruent (AB = BC and AD = CD, since B is the midpoint of AC). However, we are not given that the included angle (angle ABD) is congruent to angle CBD.
Therefore, we cannot use the SAS congruence postulate to prove that triangle ABD is congruent to triangle CBD.
Answer to part (b)
If we are also given that AD is congruent to CD, then we can use the SSS congruence postulate to prove that triangle ABD is congruent to triangle CBD.
The SSS congruence postulate states that two triangles are congruent if they have three pairs of corresponding sides congruent.
In this case, we have three pairs of corresponding sides congruent (AB = BC, AD = CD, and BD = BD). Therefore, we can use the SSS congruence postulate to prove that triangle ABD is congruent to triangle CBD.
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Elmo buckets made 54 out of 80 free throw .What percent did he miss
Answers
Answer:
67.50%
Step-by-step explanation:
We can prove that the answer is correct by taking 67.50 percent of 80 to get 54:
(80 x 67.50)/100 = 54
Note that our calculator rounds the answers up to two decimals if necessary. Once again, the answer is as follows:
67.50%
The distance around a circle is 56.55 meters long. What is the diameter of the circle?
Answers
Answer: Diameter of circle = 18m
Explanation:
Given that distance around a circle is = 56.55 meter
The distance around a circle on the other hand is called the circumference .
That means Circumference = 56.55 m
We know the formula of circle's circumference= 2πr
where r is the radius and 2r is diameter of the circle
So,
2πr = 56.55
divide by π both the side
2r = [tex] \frac{56.55*7}{22} [/tex]
Value of π = [tex] \frac{22}{7} [/tex]
2r = 17.993 ≈ 18 m
Diameter of circle = 18m
Michaela caught 3 fish, which weigh a total 19 1/2 pounds. One fish weighs 7 5/8 pounds and another weighs 5 3/4 pounds. How much does the third fish weigh?
Answers
1) 19 4/8= 156/8 Then add the second. 2) 7 5/8= 61/8 one and the third
3) 5 6/8= 46/8 one. Which is
15/8. Then, subtract your answer and the first one. You get 141. Simplify. 17 5/8
1.2 decreased by 40%
Answers
1.2 - 0.48 = 0.72
Solution = 0.72
I hope this helps
Please help!!!
What sum of money will yield a simple interest of Rs.1155 in 3 years 6 months at 11% per annum .
Answers
Answer:
Rs.833.94
Step-by-step explanation:
To solve for the sum of money or principal, we use the formula:
[tex]P=\dfrac{A}{1+rt}[/tex]
The current variables we have are:
A = Rs.1,155
r = 11% or 0.11
t = 3.5
Now let's plug the variables into the formula.
[tex]P=\dfrac{A}{1+rt}[/tex]
[tex]P=\dfrac{1,155}{1+(0.11)(3.5)}[/tex]
[tex]P=\dfrac{1,155}{1+0.385}[/tex]
[tex]P=\dfrac{1,155}{1.385}[/tex]
[tex]P=Rs.833.94[/tex]
Explain the advantage of creating a linear function from a set of data; why bother to do this?
Answers
Here is an example. Height and shoe size have a linear relationship. Let's say you plot the point (height in inches, shoe size in US women's sizes) for 50 people or so. You would see a strong linear relationship. The points wouldn't make a perfect line but very close to it. As height increases so does shoe size and it does so in a linear way. Now if we call the height h and the shoe size s then we would have an equation that relates h and s. So that if we wanted to know the shoe size of someone 96 inches (8 feet high) tall we could get that (or very close to it) from the equation even if there was no one in our sample that was that tall. Similarly we could solve for height if we knew shoe size.
Which of the following represents the most accurate estimation of 375+147
Answers
rounded to the nearest hundred is 500
The first person who answers correctly gets thanks and braniy!
1. The figures shown are similar. What is the scale factor? [Image one]
2. The figures shown are similar. What is the scale factor? [Image 2]
Answers
One
Scale factor = 21/14 = (3*7)/(2*7) = 3/2 the sevens cancel out.
Two
Scale factor = 24/18 = (6 *4) / (6 * 3) The 6s cancel out
Scale factor = 4/3
The image on a movie poster was shrunk to make the DVD cover art for the movie, so that the cover art is a scale image of the poster. The poster is 36 inches wide, and the DVD cover art is 6 inches wide. If the diagonal of the poster is 4 feet, what is the diagonal of the DVD cover art?
Answers
Now that we have our proportionality constant lest apply it to the diagonal of the poster to find the diagonal of the DVD cover. But notice that the diagonal of the poster is in feet not inches, so we need to convert 4 feet to inches first. Remember that 1 foot = 12 inches, so lets use that proportion to set up our conversion fraction:
[tex](4feet)( \frac{12inches}{1 foot} )= 48inches[/tex]
The only thing left now is shrunk, divide, the diagonal by our proportionality constant [tex]k[/tex]
[tex] \frac{48}{k} = \frac{48}{6} =8[/tex]
We can conclude that If the diagonal of the poster is 4 feet, the diagonal of the DVD cover will be 8 inches.
Ravi is driving 440 miles to visit his grandma. He drives at a rate of 55 miles per hour. How many hours will it take him to get 34 of the way there?
Answers
Answer:
The answer is 6 hours
Step-by-step explanation:
;)
Gabe filled 5 glasses of the same size with ice tea from a full 64-ounce pitcher. There were 3 ounces left in the pitcher. Which equation and solution give the number of ounces, s, in each glass?
Answers
Answer:
The number of ounces in each glass is [tex]12.2\ ounces[/tex]
Step-by-step explanation:
Let
s-------> the number of ounces in each glass
we know that
To get the number of ounces in each glass, subtract the amount of tea left in the pitcher from the total amount of tea and divide the result by the number of glasses.
so
The equation that represent the situation is
[tex]s=(64-3)/5[/tex]
[tex]s=(61)/5=12.2\ ounces[/tex]
Answer:
Step-by-step explanation:
Please help offering All my pts and brainliest answer
(06.02 LC)Which of the following algebraic expressions can be used to express the statement "one less than x squared?"
1 − x2
x2 − 1
1 − 2x
2x − 1
Answers
Algebraic expression can be used to express the statement one less than x squared is option (B) [tex]x^{2} -1[/tex]
What is Algebraic expression?In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.
Given,
one less than x squared is
[tex]x^{2} -1[/tex]
Hence, the algebraic expression can be used to express the statement one less than x squared is option (B) [tex]x^{2} -1[/tex]
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which names the opposite and absolute value of 12
Answers
Absolute value: |12| = 12
A rope that is 2 feet and 6 inches long is cut into 3 strips in a ratio of 2: 3: 5 How long is the longest piece How much longer is the longest piece than the shortest one?
Answers
Semi annually means how many times a year?
Answers
Over several months, a meteorologist recorded a total snowfall of 8.6 centimeters. During this period, the average monthly snowfall was 4.3 centimeters. For how many months did the meteorologist collect measurements of the snowfalls?
Answers
An economy package of cups has 200 green cups. If the green cups are 10% of the total package, how many cups are in the package?
Answers
Final answer:
Set up a proportion where 10% of the total number of cups equals 200 green cups, then calculate to find that there are 2000 cups in the entire package.
Explanation:
To find the total number of cups in the package when 200 green cups represent 10% of the total, we can set up a simple proportion. Here, 10% corresponds to the number of green cups we know about. We need to find 100% to discover the total number of cups in the package.
The proportion we'll set up is:
10% / 200 cups = 100% / x cups
To solve for x (the total number of cups), we will divide 200 cups by 10% to find the value of 1% and then multiply by 100%:
1% of total = 200 cups / 10
x (total cups) = (200 cups / 10) × 100
Perform the calculation:
x = 20 cups × 100
x = 2000 cups
So, there are 2000 cups in the total package.
What is the median value of the data set shown on the line plot?
Answers
The answer is 6. I'm just adding this to help anyone else struggling with this quiz.
A triangular prism and two nets are shown:
Which is the correct net of the prism and what is the surface area of the prism?
Answers
surface area of the prism is
Surface area = Area of two triangular faces + Area of bottom rectangle + Area of two side rectangles
View attachment
Hope this helps
The correct net of the prism is net A and the surface area of the prism is 510 square inches
How to determine the surface areaTo calculate the area of the triangular prism, we make use of the net A
Start by calculating the area of the rectangle.
The dimension of the rectangle is (5 + 12 + 13) by 15
So, the area of the rectangle is:
[tex]Area = (5 + 12 + 13) * 15[/tex]
[tex]Area = 450[/tex]
Next, calculate the area of the two congruent triangles of base 5 and height 12
[tex]Area = 2 * 0.5 * (5 * 12)[/tex]
[tex]Area = 60[/tex]
Sum both areas
[tex]Total = 450 + 60[/tex]
[tex]Total = 510[/tex]
Hence, the surface area of the prism is 510 square inches
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you have to find the volume of this figure
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1/2 x L x H X W
1/2 x 8 x 4.5 x 30 = 540
area of top triangular pyramid
1/3 x B x H
B = 1/2 bxh = 1/2 x 8 x 4.5 = 18
1/3 x 18 x 10 = 60
total volume = 540 + 60 = 600 cubic cm
HELP EXPERTS AND GENIUSES PLS HELP
What is the best approximation for the circumference of a circle with a radius of 45 cm?
Use 3.14 to approximate pi.
1:70.65 cm
2:141.3 cm
3:282.6 cm
4:6358.5 cm
Answers
90 x 3.14 = 282.6 cm
answer is: 3:282.6 cm
Answer:
282.6
Step-by-step explanation:
find the measures of the numbered angles in each figure
Answers
2 is 90 - 27 = 63
3 63 angles 2 and 3 are in an isosceles triangle. They are opposite equal sides so the angles are equal.
A navigator plots the course a plane is currently traveling. The plane is 300 miles from its destination. If it continues on its current course it will travel 325 miles and end up 125 miles due south of its destination. To the nearest degree, how many degrees is the plane off course?
Answers
To find how many degrees off course the plane is, we must use the rules of Cosx°, which is shown in the attached image.
The plane is approximately 23° off course.
The plane in question is approximately 23 degrees off course. This calculation is derived from the tangent function in trigonometry based on the distances given.
Explanation:From the question, we understand that the plane is creating a right triangle due to its off-course direction. Using the Pythagorean theorem, the length of the hypotenuse, or the distance that the plane will travel, is 325 miles. The difference between the direct route (300 miles) and the off-course southern distance (125 miles) forms the two other sides of the triangle.
However, we're looking for the angle, not the sides. This is where trigonometry comes in. Specifically, the tangent function will be valuable here as it involves the opposite and adjacent sides of a right triangle (the off-course southern distance and the direct route distance). If we let the 'off-course' angle be θ, then we have:
Tan(θ) = (distance south / direct distance) = (125 miles / 300 miles)
In order to find the angle θ from this equation, we'll need to use the inverse tangent function.
θ = atan(125/300) = 22.61986495 degrees.
Therefore, to the nearest degree, the plane is approximately 23 degrees off course.
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Help with this question please!!
Answers
[tex]3(6x) = 18x[/tex]
The third one is answer because it simplifies to:
[tex]2x(9) = 18x[/tex]
Those are all your answers: Option 1 and Option 2.
What’s the answer? Thank You
Answers
25 square inches --> straight line across
Each side of the square below is 20 centimeters. The area of the circle inside the square is about 314 square centimeters.
a.43/200
b.43/157
c.157/200
d.200/157
Answers
Answer:
It would be 157/200
Step-by-step explanation:
The gent in the comments