What are the features of the quadratic function f(x) = x^2 + 10x + 21?
A) Vertex = (-5,-4), y-intercept = (0,21), x-intercepts = (-7,0) and (-3,0), axis of
symmetry is x = -5
B)
Vertex = (5,4), y-intercept = (0,-21), x-intercepts = (-7,0) and (-3,0), axis of
symmetry is x = 5
C)
Vertex = (-4,-5), y-intercept = (0,21), x-intercepts = (-7,0) and (-3,0), axis of
symmetry is x = -4
D)
Vertex = (-5,-4), y-intercept = (21,0), x-intercepts = (3,0) and (7,0), axis of
symmetry is x= -5
Answers
The features of the quadratic function f(x) = x^2 + 10x + 21 are Vertex = (-5,-4), y-intercept = (0,21), x-intercepts = (-7,0) and (-3,0), axis of symmetry is x = -5 so option (A) will be correct.
What is a quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.
For example 3x² + 6x + 8 = 0 here x has highest term as 2 and coefficient of x² is not zero.
The standard form of a quadratic equation is ax² + bx + c
The x vertex is given -b/2a
So,
x-vertex = -10/2 = -5
So y = (-5)² + 10(-5) + 21 = -4
So vertex is (-5, -4)
The Y-intercept is given as (0,y)
So,
y = 21
Therefore
y-intercept = (0,21)
the x-intercept is given as (x,0)
So,
x = -7 , -3
Therefore
x-intercepts = (-7,0) and (-3,0)
The Axis of symmetry is given by -b/2a
So,
⇒ -10/2 = -5
Hence "Vertex = (-5,-4), y-intercept = (0,21), x-intercepts = (-7,0) and (-3,0), axis of symmetry is x = -5".
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Related Questions
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
Answer 17.67
Step-by-step explanation:
x = ticket price
y = number of spectators (in thousands)
\(\frac{y-23000}{x-10} = \frac{26-23}{7-10} = -1\)
R = revenue (in thousands)
R = xy = x * (23-3(x-10))
= x * (23-3x+30)
R' = 53-3x
R'' = - 3
R'=0 (-) x = 53/3 = 17.67 (local maximum)
Who was in command of the Texan forces at the Alamo
Answers
Travis' famous letter, addressed to "The People of Texas and All Americans in the World," in which he passionately appealed for reinforcements and vowed to "never surrender or retreat," has become a symbol of the fortitude and sacrifice displayed by the Texan defenders at the Alamo.
The commander of the Texan forces at the Alamo during the famous battle in 1836 was Colonel William B. Travis. Travis, a lawyer and soldier, was chosen as the leader of the Texan garrison at the Alamo, a former mission turned fortress in San Antonio, Texas. He assumed command of the Texan forces in early 1836 and played a crucial role in the defense of the Alamo against the Mexican army led by General Santa Anna.
Travis and his men, along with notable figures such as James Bowie and Davy Crockett, bravely defended the Alamo against overwhelming odds for thirteen days. Despite their courage and determination, the Texan defenders were ultimately overrun by the Mexican forces on March 6, 1836, and suffered heavy casualties, including the deaths of Travis, Bowie, and Crockett.
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What is the solution to the linear equation?
2/5+p=4/5+3/5p
Answers
Answer:
p=1
Step-by-step explanation:
Rearrange terms
Combine multiplied terms into a single fraction
Subtract 2/5 from both sides of the equation
Simplify
Multiply all terms by the same value to eliminate fraction denominators
sorry if its wrong
You have how substitute -3x+14y=-18
Answers
9514 1404 393
Answer:
(b) (6, 0)
Step-by-step explanation:
You are given the value of x. Substitute that in the other equation and find the value of y.
-3x +14y = -18
We know x=6 from the second given equation, so ...
-3(6) +14y = -18
Add 18 to both sides
14y = 0
Divide by 14
y = 0
Then the solution is ...
(x, y) = (6, 0)
What is the difference of
5
6
−
5
12
? Use the fraction strip to help.
One whole fraction strip is equal to six one-sixth fraction strips. It is also equal to twelve one-twelfth fraction strips.
A.
0
B.
5
12
C.
7
12
D.
5
6
Answers
The difference of 5/6 - 5/12 is 5/12..
What is a fraction?A fraction consisting of a quotient and a remainder is a mixed fraction. we can convert the mixed fraction to an improper fraction by first dividing the numerator by the denominator and then taking the quotient as whole number and the remainder as the numerator of the proper fraction keeping the denominator same.
In this question, we need to apply real algebra properties to find the result of a basic operation between two fractions, whose procedure is shown below:
Given
5/6 - 5/12
Now multiply by 2 in fraction 5/6
10/12 - 5/12
5/12
The difference is 5/12.
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Write a quadratic equation in factored form if it has x-intercepts 2 and -1 and y-intercept 6.
Answers
We have to write a quadratic equation, in factored form, that has an x-intercept at x=2 and x=-1, and a y-intercept 6.
As the x-intercepts are the roots of the function, we can write the equation as:
\(y=a(x-2)(x+1)\)The parameter a will be defined in order to have a y-intercept at y=6. That means that, when x is 0, the value of the function is y=6.
Then, we can replace x with 0 and y with 6 and find the value of a:
\(\begin{gathered} y=a(x-2)(x+1) \\ 6=a(0-2)(0+1) \\ 6=a(-2)(1) \\ 6=-2a \\ a=\frac{6}{-2} \\ a=-3 \end{gathered}\)With the value of a=-3, we can write the factorized form of the equation as:
\(y=-3(x-2)(x+1)\)Graph:
Answer: y=-3(x-2)(x+1)
-8(d10) + 42 = 50
Equation solved algebraically
Answers
Answer:
d= -11
firstly you distribute, then you add the numbers, add 38 to both sides, simplify, divide both sides by the same factor, divide the numbers and that's the total
Jesaria can jump rope 42 times in 20 seconds at this rate how many times can she jump rope in 2 minute
Answers
Jesaria jump rope 42 times in 20 seconds
So in 01 second jump rate=42/20
In 01 minute (60 second)
she will jump = 42x60/20
=126 times answer
What’s the correct answer for this question?
Answers
Answer:
Step-by-step explanation:
the event of drawing a spade card
please help vvvvvvvvvvv
Answers
Answer:
17
Step-by-step explanation:
since you are subtracting a negative number it reverses, so you actually ADD the two together
so, 12 1/2 + 4 1/2
add the whole numbers first;
12+4=16
then fractions:
1/2 + 1/2= 1
then all together;
16+1=17!
Answer:
17
Step-by-step explanation:
hope I can help :)
A rectangular room is 14 feet by 20 feet. A rectangular rug is placed in the room so that a 2-foot border of floor around the edge of the room is not covered by the rug. What is the area of the rug?
Answers
Answer:
the rug should be 10 feet by 16 feet
this makes the area 160 foot squared
Step-by-step explanation:
there is a 2 foot border on each side so the total area loses 4 feet from length. this gives 10 feet by 16 feet.
160
top correct lolssssss
The base of the mountain is 6,500 feet above sea level and AB measures 230 feet across. Given that the measurements for QAP is 20° and QBP is 35°, how far above sea level is peak P ? Express your answer to the nearest foot.
Height above sea level:
Answers
Answer:
6610
Step-by-step explanation:
We have tan(X) = opposite/ adjacent
tan(QBP) = PQ/BQ
tan(35) = PQ/BQ ---eq(1)
tan(QAP) = PQ/AQ
tan(20) = \(\frac{PQ}{AB +BQ}\)
\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)
230*tan(20) + PQ*tan(20)*tan(35) = PQ
⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)
⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]
\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)
\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)
PQ = 110.4
≈110
Height above sea level = 6500 + PQ
6500 + 110
= 6610
Find a quadratic function that includes the set of values below.
(0,7), (2,17), (3,16)
The equation of the parabola is Y
Answers
Y = aX^2 + bX + c
where Y is the output (dependent variable), X is the input (independent variable), and a, b, and c are constants that we need to solve for.
We can plug in the three sets of values given into this equation to get three equations:
7 = a(0)^2 + b(0) + c
17 = a(2)^2 + b(2) + c
16 = a(3)^2 + b(3) + c
Simplifying each equation, we get:
7 = c
17 = 4a + 2b + c
16 = 9a + 3b + c
Substituting c = 7 from the first equation into the other two equations, we get:
17 = 4a + 2b + 7
16 = 9a + 3b + 7
Simplifying these equations, we get:
4a + 2b = 10
9a + 3b = 9
We can solve this system of equations using substitution or elimination to find the values of a and b. I'll use elimination:
Multiplying the first equation by 3 and the second equation by -2, we get:
12a + 6b = 30
-18a - 6b = -18
Adding the two equations, we get:
-6a = 12
a = -2
Substituting a = -2 into one of the equations we got earlier (e.g. 4a + 2b = 10), we get:
4(-2) + 2b = 10
-8 + 2b = 10
2b = 18
b = 9
So the values of a and b are -2 and 9, respectively. Substituting these values into the general form of the quadratic function, we get:
Y = -2X^2 + 9X + 7
Therefore, the equation of the parabola is:
Y = -2X^2 + 9X + 7
Pls mark brainliest
Candy buys 20 ounces of mixed nuts. She puts
an equal number of ounces in each of 3 bags.
How many ounces of mixed nuts will be in each
bag? Write the answer as a whole number and
fraction.
Answers
Answer:
20/3 ≈ 6.66
Step-by-step explanation:
20÷3= 20/3 ≈6.66
Help with math problems
Answers
The vertex form of the quadratic equations in standard form are, respectively:
Case 9: y = 2 · (x + 2)² - 12
Case 10: y = - (1 / 2) · (x + 3 / 4)² + 33 / 32
Case 11: y = 3 · (x - 4 / 3)² - 16 / 3
Case 12: y = - 3 · (x - 3)²
Case 13: y = (x - 4)² + 3
Case 14: y = (x - 1)² - 7
Case 15: y = (x + 3 / 2)² - 9 / 4
Case 16: 2 · (x + 1 / 4)² - 1 / 8
Case 17: y = 2 · (x - 3)² - 7
Case 18: y = - 2 · (x + 1)² + 10
How to derive the vertex form of a quadratic equationIn this problem we find ten cases of quadratic equation in standard form, whose vertex form can be found by a combination of algebra properties known as completing the square. Completing the square consists in simplifying a part of the quadratic equation into a power of a binomial.
The two forms are introduced below:
Standard form
y = a · x² + b · x + c
Where a, b, c are real coefficients.
Vertex form
y - k = C · (x - h)²
Where:
C - Vertex constant(h, k) - Vertex coordinates.Now we proceed to determine the vertex form of each quadratic equation:
Case 9
y = 2 · x² + 4 · x - 4
y = 2 · (x² + 2 · x - 2)
y = 2 · (x² + 2 · x + 4) - 12
y = 2 · (x + 2)² - 12
Case 10
y = - (1 / 2) · x² - 3 · x + 3
y = - (1 / 2) · [x² + (3 / 2) · x - 3 / 2]
y = - (1 / 2) · [x² + (3 / 2) · x + 9 / 16] + (1 / 2) · (33 / 16)
y = - (1 / 2) · (x + 3 / 4)² + 33 / 32
Case 11
y = 3 · x² - 8 · x
y = 3 · [x² - (8 / 3) · x]
y = 3 · [x² - (8 / 3) · x + 16 / 9] - 3 · (16 / 9)
y = 3 · (x - 4 / 3)² - 16 / 3
Case 12
y = - 3 · x² + 18 · x - 27
y = - 3 · (x² - 6 · x + 9)
y = - 3 · (x - 3)²
Case 13
y = x² - 8 · x + 19
y = (x² - 8 · x + 16) + 3
y = (x - 4)² + 3
Case 14
y = x² - 2 · x - 6
y = (x² - 2 · x + 1) - 7
y = (x - 1)² - 7
Case 15
y = x² + 3 · x
y = (x² + 3 · x + 9 / 4) - 9 / 4
y = (x + 3 / 2)² - 9 / 4
Case 16
y = 2 · x² + x
y = 2 · [x² + (1 / 2) · x]
y = 2 · [x² + (1 / 2) · x + 1 / 16] - 2 · (1 / 16)
y = 2 · (x + 1 / 4)² - 1 / 8
Case 17
y = 2 · x² - 12 · x + 11
y = 2 · (x² - 6 · x + 9) - 2 · (7 / 2)
y = 2 · (x - 3)² - 7
Case 18
y = - 2 · x² - 4 · x + 8
y = - 2 · (x² + 2 · x - 4)
y = - 2 · (x² + 2 · x + 1) + 2 · 5
y = - 2 · (x + 1)² + 10
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Question no 59
Need solution
Answers
The area of the shaded region is 104 cm²
How to determine the areaFirst, we need to know that the area of a circle is calculated using the formula;
A = πr²
Such that the parameters of the formula are;
A is the area of the circler is the radiusFirst, let us find the area of the small circle
Area = 3.14 × 4²
Find the square value and multiply, we have;
Area = 50.24cm²
Area of the large circle = 3.14 × 7²
Find the square value and multiply
Area = 153. 86cm²
Area of the shaded region = Area of large circle - area of small circle
= 153.86 - 50.24
= 104 cm²
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Ryan’s grandparents bought him a new basketball. Ryan wants to know if the ball is the same size as the ball his basketball league uses. The volume of the ball is 295.6 cubic inches. What is the circumference of Ryan’s new basketball? Use 3.14 for pi
.
Answers
Thus, the circumference of Ryan’s new spherical basketball is found as: 52.752 in.
Explain about the circumference:The perimeter of a polygon, including a square or rectangle, is the distance around it (P). On the opposing hand, the circumference of a circle is the distance around it (C). As a result, the circular circumference is the length of a circle's edge in linear terms.
Given data:
Volume of ball = 295.6 cubic inches.As the ball is in the shape of sphere.
Let r be the radius of sphere:
Volume of sphere = 4/3 * π * r³
295.6 = 4/3 * 3.14 * r³
r³ = (295.6 * 3)/(4*3.14)
r³ = 70.60
r = 8.40 in
circumference = 2 * π * r
circumference = 2 * 3.14 * 8.40
circumference = 52.752 in
Thus, the circumference of Ryan’s new spherical basketball is found as: 52.752 in.
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What’s the correct answer for this question ?
Answers
Answer:
B:
Step-by-step explanation:
P(A or B) = P(A)+P(B)-P(A and B)
0.5 = 0.4 + P(B) -0.2
P(B) = 0.5-0.4+0.2
P(B) = 0.3
Nola hiked down a trail at a steady rate for 10 minutes. Her change in elevation was -170 feet. Then she continued to hike down another 20 minutes at a different rate. Her change in elevation for this part of the hike was -260 feet. During which portion of the hike did she walk down at a faster rate?
PLEASE HELP
Answers
170/10 = 17
I turned the -170 into a positive because when you divide them, you get 17 miles per minute, you can’t get -17 miles.
Then, you divide 260 by 20, and you get :
260/20 = 13
So, 17>13
Which means that’s Nola walked faster when she walked for 10 minutes.
I’m pretty sure that this is the answer, hope this helps. Do you mind making this brainliest?
What is the image of (1, 0) after a dilation by a scale factor of 4 centered at the
origin?
Answers
Answer:
(4, 0)
Step-by-step explanation:
You want the image point coordinates of (1, 0) dilated by a factor of 4 centered at the origin.
DilationWhen the dilation is centered at the origin, all coordinate values are multiplied by the scale factor.
(1, 0) ⇒ 4(1, 0) = (4, 0)
The image of the point is (4, 0).
Determine a value of x for each of the following. Give answers in simplest exact form.
cos (11pi/31) = sinx
Answers
9514 1404 393
Answer:
x = 9π/62
Step-by-step explanation:
We can make use of the fact that ...
sin(x) = cos(π/2 -x)
Then ...
π/2 -x = 11π/31
π(1/2 -11/31) = x = 9π/62
What is the following sum?
5(³3√x)+9(³√x)
0 14 (√x)
14 (2√x²)
0 14 (3√x)
0
X
Answers
The solution for the given expression is 14∛x. The correct option is (C).
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given expression is as below,
5∛x + 9∛x
The given expression can be simplified as follows,
5∛x + 9∛x
Here, both the terms have equivalent variables. So, both are like terms.
As per the rules like terms can be added or subtracted keeping the variable as the same.
Thus, 5∛x + 9∛x = 14∛x
Hence, the given expression can be evaluated as 5∛x + 9∛x = 14∛x.
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Which polygons have at least one pair of parallel sides but are not parallelograms
Answers
on a number line, suppose point E has a quotient of -1, and EG = 12. what are the possible coordinates of point G?
Answers
-13, or +11, because they are both 12 places away from -1.
a histogram showing u.s. household income is highly skewed right. which of following statistics would best describe the center of the distribution? question 10 options: 1) median 2) variance 3) mean 4) mode
Answers
......,,........,.....-.......
The median would best describe the centre of the distribution for a highly skewed right histogram of US household income. The correct option is A.
What is the median?The median is the value that separates the distribution into two equal parts and is less influenced by extreme values than the mean.
Since a highly skewed right distribution has a long tail on the right side, the mean is likely to be pulled towards that tail, making it an unreliable measure of the centre.
The mode, or most frequently occurring value, may not be useful for describing the centre of a skewed distribution. The variance is a measure of the spread or dispersion of the data, not its centre.
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A smartphone costs $120. Sales tax is 5%. What is the total cost, including tax?
Answers
Answer:
$126
Step-by-step explanation:
5% of 120 is 6.
Then add it since it askes the total including tax.
6 + 120 = 126
The outside diameter of an electrical conduit is 6.3 centimeters. The thickness of the conduit is 0.4 centimeter. Find the inside diameter of the conduit. Carry the answer to one decimal place.
Answers
Answer:
5.5 cm
Step-by-step explanation:
You want the inside diameter of a conduit with an outside diameter of 6.3 cm and a wall thickness of 0.4 cm.
WallsThere is a wall at each end of the inner diameter, so it will differ from the outside diameter by twice the wall thickness:
6.3 cm - 2×0.4 cm = 5.5 cm
The inside diameter is 5.5 cm.
Which is the equation for the line in slope-intercept form if:
m = -3/2 : b = 5
y = 5x + (-3/2)
y=(-3/2)x+ 5
Oy+(-3/2) = 5x
y-5=(-3/2)x
Answers
this is because the slope and the y intercept is included in that one in the y=mx+b format.
Find the area of the shape.
Either enter an exact answer in terms of iT or use 3.14 for
and enter your answer
as a decimal.
units?
Answers
The area of the shape is 12.56 square units
How to determine the rea of the shapeFrom the question, we have the following parameters that can be used in our computation:
Radius = 2
The area of a circle is calculated as
Area = pi * r^2
Substitute the known values in the above equation, so, we have the following representation
Area = 3.14 * 2^2
Evaluate
Area = 12,56
Hence, the area is 12.56 square units
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Complete question
A circle has a radius of 2 units
Find the area of the shape.
Either enter an exact answer in terms of iT or use 3.14 for
and enter your answer
as a decimal.
units?
how do you do stuff like 20 x 0.4?? i forgot
Answers
Answer: the answer is 8.0
Step-by-step explanation: what i do is 20*4 which is 80 and i just add the decimals back in hoped this helped :))