determine the quadratic function of f whose graph is given. The vertex is (1,-3) and the y-intercept is -2

Answers

Answer 1

hmmm the y-intercept is at -2? what does that mean? well, is where the graph "intercepts" or touches the y-axis, and when that happens, x = 0, so the point is really ( 0 , -2 ).

and we know where the vertex is at. Let's assume a vertical parabola, in which case the squared variable is the "x".

[tex]\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ vertex \begin{cases} h=1\\ k=-3 \end{cases}\implies y=a(x-1)^2-3 \\\\\\ \textit{now, we also know that } \begin{cases} x=0\\ y=-2 \end{cases}\implies -2=a(0-1)^2-3 \\\\\\ 1=a(-1)^2\implies \boxed{1=a}\qquad thus\implies \begin{cases} y=1(x-1)^2-3\\ \textit{or just}\\ y=(x-1)^2-3 \end{cases} [/tex]

Related Questions

if 2 pounds of strawberries cost 4.50 how much would 3 pounds cost

Answers

6.75$ this my best answer

[tex]\bf \begin{array}{ccll} lbs&\$\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 2&4.50\\ 3&x \end{array}\implies \cfrac{2}{3}=\cfrac{4.50}{x}\implies x=\cfrac{3\cdot 4.50}{2}[/tex]

Nicholas volunteers at a local soup kitchen and he notices how quickly the kitchen is going through its stock of canned goods. Below is the graph representing the data Nicholas found. Find the slope and y-intercept of the line.

Answers

Answer:

m=-63 b=825

Step-by-step explanation:

The slope of the line would be - [m] = - 63 and the [y] intercept is - [c] = 835.

What is the general equation of straight line? What is a mathematical function, equation and expression?straight line : The general equation of a straight line is -

[y] = mx + c

function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.

Given is that Nicholas volunteers at a local soup kitchen and he notices how quickly the kitchen is going through its stock of canned goods.

It is given that a graph has number of days on the x - axis and number of canned goods on the y-axis. The line goes through points (2, 699) and (8, 321). The slope of the line can be written as -

[m] = (321 - 699)/(8 - 2)

[m] = -378/6

[m] = - 63

For the point (2, 699), we can write -

y = - 63x + c

699 = - 63 x 2 + c

699 = -126 + c

c = 699 + 126

c = 835

Therefore, the slope of the line would be - [m] = - 63 and the [y] intercept is - [c] = 835.

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{Complete question -

A graph has number of days on the x-axis and number of canned goods on the y-axis. A line goes through points (2, 699) and (8, 321).

Nicholas volunteers at a local soup kitchen and he notices how quickly the kitchen is going through its stock of canned goods. Below is the graph representing the data Nicholas found.

Find the slope and y-intercept of the line.}

Suppose e(x) = 3 and e[x(x − 1)] = 27.5. (a) what is e(x2)? [hint: first verify that e[x(x − 1)] = e[x2 − x] = e(x2) − e(x).]

Answers

52(ex) would be your answer

6-1. let x have a poisson distribution with a mean of 4. find (a) p(2≤x≤5). (b) p(x≥3). (c) p(x≤3).

Answers

The mean of a Poisson distribution coincides with its rate parameter, so [tex]\lambda=4[/tex]. We have a PMF of

[tex]f_X(x)=\dfrac{e^{-4}4^x}{x!}[/tex]

So,

a. [tex]\mathbb P(2\le X\le5)=\dfrac{e^{-4}4^2}{2!}+\cdots+\dfrac{e^{-4}4^5}{5!}\approx0.6936[/tex]

b. [tex]\mathbb P(X\ge3)=\dfrac{e^{-4}4^3}{3!}+\dfrac{e^{-4}4^4}{4!}+\cdots\approx0.7619[/tex]

c. [tex]\mathbb P(X\le3)=\dfrac{e^{-4}4^0}{0!}+\cdots+\dfrac{e^{-4}4^3}{3!}\approx0.4335[/tex]

Determine whether or not the vector field is conservative. if it is conservative, find a function f such that f = ∇f. (if the vector field is not conservative, enter dne.) f(x, y, z) = ye−xi + e−xj + 2zk

Answers

A three-dimensional vector field is conservative if it is also irrotational, i.e. its curl is [tex]\mathbf 0[/tex]. We have

[tex]\nabla\times\mathbf f(x,y,z)=-2e^{-x}\,\mathbf k[/tex]

so this vector field is not conservative.

- - -

Another way of determining the same result: We want to find a scalar function [tex]f(x,y,z)[/tex] such that its gradient is equal to the given vector field, [tex]\mathbf f(x,y,z)[/tex]:

[tex]\nabla f(x,y,z)=\mathbf f(x,y,z)[/tex]

For this to happen, we need to satisfy

[tex]\begin{cases}f_x=ye^{-x}\\f_y=e^{-x}\\f_z=2z\end{cases}[/tex]

From the first equation, integrating with respect to [tex]x[/tex] yields

[tex]f_x=ye^{-x}\implies f(x,y,z)=-ye^{-x}+g(y,z)[/tex]

Note that [tex]g[/tex] *must* be a function of [tex]y,z[/tex] only.

Now differentiate with respect to [tex]y[/tex] and we have

[tex]f_y=-e^{-x}+g_y=e^{-x}\implies g_y=2e^{-x}\implies g(y,z)=2ye^{-x}+\cdots[/tex]

but this contradicts the assumption that [tex]g(y,z)[/tex] is independent of [tex]x[/tex]. So, the scalar potential function does not exist, and therefore the vector field is not conservative.

Final answer:

To ascertain if a vector field is conservative or not, you need to calculate the curl of the field or integrate over the components of the vector field. If the curl is zero, it's conservative. If the curl isn't zero or an integral doesn't exist, the field is not conservative.

Explanation:

To determine if the vector field f(x, y, z) = ye−xi + e−xj + 2zk is conservative, we need to find if there exists a function f such that f is the gradient (denoted by ∇) of f. This can be done by checking if the cross product of the vector field is equal to zero, which signifies that the field is conservative.

First, we calculate the curl (∇ x F) of the vector field, which gives us the derivatives of the field components. If the curl is zero, then the vector field is conservative. If it is not zero, this indicates that the vector field is non-conservative.

Alternatively, we can integrate over the components of the vector field to try and find a potential function. If an integral exists, then we can say that the vector field is conservative.

However, if it fails these conditions, then the vector field is not conservative and the function f does not exist for it (dne). Thus, in the case where the vector field is not conservative, enter 'dne'.

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Given f(x) = x^2 - 10x + 22, what is the range of f?

Answers

The range is all the possible y-values.

For a parabola that opens up, it is everything greater than the vertex.

If the vertex is (h,k) then the range is y >= k.

Vertex can be found using completing the square:
[tex]x^2 -10x +22 \\ \\ (x^2 -10x + (\frac{-10}{2})^2) +22 - (\frac{-10}{2})^2 \\ \\ (x^2 -10x+25) +22-25 \\ \\ (x-5)^2 - 3[/tex]
(h,k) = (5,-3) ------> Range is y >= -3

Vertex may also be found using formula [tex]h = \frac{-b}{2a} [/tex]
a = 1, b = -10, c = 22
[tex]h = \frac{10}{2} = 5[/tex]
[tex]k = 5^2 - 10(5) +22 \\ \\ k = 25 -50+22 \\ \\ k = -3[/tex]
------> Range is y >= -3

f(x)=x2-10x+22 domain of f

Answer: all real numbers

Range of F

Answer: y> -3

A school conference room can seat a maximum of 83 people. The principal and two counselors need to meet with the school’s student athletes to discuss eligibility requirements. If each student must bring a parent with them, what is the maximum number of students that can attend each meeting?

Answers

if you have only 83 seats, and 3 of which are being occupied by the principal and two counselors, (3 people that will always be at the meetings) you only have 80 seats for the students and the parents. If each student brings only 1 parent with them, divide 80 by 2 ( 2 is a pair of student and parent ) you will have 40 seats. You can only invite 40 Students

Answer:

The maximum number of students that can attend each meeting is:

Step-by-step explanation:

A school conference room can seat a maximum of 83 people.

The principal and two counselors need to meet with the school’s student athletes to discuss eligibility requirements.

Let there be x students,there will be x parents

that means x+x+3≤83

Subtracting both sides by 3,we get

2x≤80

dividing both sides by 2,we get

x≤40

Hence, the maximum number of students that can attend each meeting is:

The Perez family has a rectangular fish tank how much water will the tank hold if it's length is 3 feet, its width is 2 feet and its height is 3 feet

A) NONE
B) 18 cubic feet
C) 3 cubic feet
D) 6 cubic feet
E) 9 cubic feet

Answers

V = 3 x 2 x 3 = 18
answer
B) 18 cubic feet

The measure of arc XZ is 28° what is the measure of XYZ

Answers

Arc XZ is marked in red (see the image attachment)
Angle XYZ is marked in blue

It turns out that angle XYZ is exactly half the measure of arc XZ. This is due to the inscribed angle theorem. Angle XYZ is an inscribed angle that cuts off, or subtends, arc XZ.

measure of arc XZ = 28 degrees
measure of angle XYZ = (1/2)*(measure of arc XZ)
measure of angle XYZ = (1/2)*(28 degrees)
measure of angle XYZ = 14 degrees

Answer: D) 14 degrees

the sum of two numbers is 18 . the difference of the two numbers is -2 find the numbers

Answers

a and b is a numbers
a + b = 18
a - b = -2

2a = 16
a = 8

8 + b = 18
b = 10

6578 divided 34

20\5

Answers

0.0037942 is your answer

Answer:

263.56 :)

Step-by-step explanation:

what is r^m divided by r^m equal to.

Answers

1, everything divided by itself is 1

Solve for the distance between (522, 1322) and (9000, -1337) to the third decimal.

Answers

[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 522}}\quad ,&{{ 1322}})\quad % (c,d) &({{ 9000}}\quad ,&{{ -1337}}) \end{array} \\\\\\ % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\\\\ -------------------------------\\\\ d=\sqrt{(9000-522)^2+(-1337-1322)^2}\\\\\\ d\sqrt{8478^2+(-2659)^2} \\\\\\ d=\sqrt{71876484+7070281}\implies d=\sqrt{78946765} \\\\\\ d\approx 8885.199209922\implies d\approx 8885.199[/tex]

Mr. and Mrs. Zeller close on a 20 year home loan for $150,000. The monthly payment with no points is $1,160, but if they buy a point it is $1,150. What might you infer if Mr.and Mrs. Zeller choose not to buy a point? a. They plan to sell the house at the end of 5 years. b. They plan to sell the house at the end of 15 years. c. They plan to sell the house at the end of 20 years. d. They plan to sell the house at the end of 25 years.

Answers

the answer is A. they plan to sell the house at the end of 5 years

Answer:

the answer is A they plan to sell it in 5 years

Step-by-step explanation:

Which three statements would produce the truth value F when p is true and q is false?

A. p -> q
B. ~p/\~q
C. p->~q
D. q\/~p
C. p/\~q
please help

Answers

B. If [tex]p[/tex] is true, then [tex]\sim p[/tex] (NOT [tex]p[/tex]) is false; If [tex]q[/tex] is false, then [tex]\sim q[/tex] is true. Then [tex]\sim p\land\sim q[/tex] must be false, because both arguments are not true.

Answer with Step-by-step explanation:

p is true then ~p is false.

q is false then ~q is true.

A. p -> q

if p is true and q is false then this gives false truth value.

Hence, here truth value is F

B. ~p/\~q

if any one of them is false then it gives false truth value.

Hence, here truth value is F(since,~p is false)

C. p->~q

true statement implies a true statement hence, truth value will be true

Hence, here truth value is T(p true implies ~q true)

D. q\/~p

if any one of them is true then compound statement is true.

Hence, here truth value is F(since, ~p and q both are false)

E. p/\~q

if both true then compound statement is also true.

Hence, here truth value is T(since p and ~q both are true)

An object's position is given by x(t) = 5 + 10 t 2. what is its acceleration after 5 s

Answers

Final answer:

The acceleration after 5 seconds is 20 m/s^2.

Explanation:

To find the acceleration, we need to take the second derivative of the position function.

x(t) = 5 + 10t^2

Taking the derivative with respect to time, we get:

v(t) = 20t

Taking the derivative again, we get the acceleration:

a(t) = 20

Therefore, the acceleration after 5 seconds is 20 m/s^2.

Factor out the coefficient of the variable. The expression 2.2x +4.4 factored is

Answers

2.2(x+2) is the answer

whats the nearest tenth to -61 square root

Answers

well, the square root of a negaitve number will be an imaginary number
that is, i=√-1

so we can write
[tex]\sqrt{-61}=(\sqrt{-1})(\sqrt{61})=(i)(\sqrt{61})[/tex] [tex] \sim (i)(7.81) \sim 7.8i[/tex]

Hello!
the √(-61) is a complex number √61i

But if you wish to find the value of an irrational and imaginary number, I will give you the approximate answer.

[tex] \sqrt{-61} \to \sqrt{-1*61} \to \sqrt{-1} * \sqrt{61} \to i* \sqrt{61} \to i*7,81024...\: \boxed{\approx 7.8i}[/tex]

Find the missing number of each unit rate

Answers

4/2 = 2/1
6/2 = 3/1
12/4 = 3/1
if the last on is negative it would -24/8 = -3/1 if positive 3/1 hope this helps remember you would reduce your fraction

4/2 reduces to 2/1.

12/4 reduces to 3/1

Can you do the remaining problems?

You've got 60 homework problems to do and it took you 10 minutes to do eight of them. At that rate, how long will it take?

Answers

10 minutes : 8 problems
x minutes : 60 problems
10 * 60/8 = 150/2 = 75 minutes for 60 problems

about 75 minutes because if you divide 60 by 8, you get 7.5, 7.5x10=75 so that is your answer

MARIA WALKED 4.035 KILOMETERES. WHAT IS 4.035 WRITTEN IN AS EXPANDED FORM ?

Answers

Here's my interpretation: 4 whole km, plus zero tenths of a km, plus 3 hundredths of a km, plus 5 thousandths of a km.

Answer:

[tex](4 \times 1)+(3 \times \frac{1}{100})+(5 \times \frac{1}{1000})[/tex]

Step-by-step explanation:

Given : MARIA WALKED 4.035 KILOMETERS.

To Find :WHAT IS 4.035 WRITTEN IN AS EXPANDED FORM ?

Solution :

Number = 4.035

The numbers after decimals when read from first to last has positions tenth , hundredth , thousandth and so ...

The number before the decimal part has positions ones , tens , hundreds and so on when read from last to first

Now 4 is at ones place

0 is at tenth place

3 is at hundredth place

5 is at thousandth place

So, Expanded form : [tex](4 \times 1)+(3 \times \frac{1}{100})+(5 \times \frac{1}{1000})[/tex]

Amanda can jog 18 miles in 5 hours. At this rate, how many miles can Amanda jog in 4 hours?

Answers

18 = x
__ __
5 4
x = 18•4 / 5
72/5 = 14.4 final answer

we know that

Amanda can jog [tex]18[/tex] miles in [tex]5[/tex] hours

by proportion

Find the number of miles that Amanda can jog in [tex]4[/tex] hours

[tex]\frac{18}{5} \frac{miles}{hours} =\frac{x}{4} \frac{miles}{hours} \\ \\5*x=18*4 \\ \\x=72/5 \\ \\ x=14.4\ miles[/tex]

therefore

the answer is

[tex]14.4\ miles[/tex]

You make a large bowl of salad to share with your friends. Your brother eats 1/3 of it before they come over. What fractional portion of the original bowl of salad does each friend receive?

Answers

How many friends are there?

Answer:

[tex]\frac{2}{3x}[/tex]

Where, x = total friends

Step-by-step explanation:

Given,

The part of the salad has eaten = [tex]\frac{1}{3}[/tex]

Total part of the salad = 1,

Thus, the remaining part of the salad = original part - part has eaten

[tex]=1-\frac{1}{3}[/tex]

[tex]=\frac{3-1}{3}[/tex]

[tex]=\frac{2}{3}[/tex]

If there are x friends,

Then the portion of the original bowl of salad received by each friend

[tex]=\frac{\text{Remaining part}}{\text{Total friends}}[/tex] [tex]=\frac{2}{3x}[/tex]

A geologist have two rocks on a scale that weighs 2 1/2 lbs together rock a was 1/7 of a the total weight how much did rock a weight

Answers

Final answer:

By using the given fraction of rock 'a' against the total weight of two rocks, we can find that rock 'a' weighs approximately 0.357 lbs.

Explanation:

The student's question involves calculating the weight of a rock, given as a fraction of a total weight. In this case, they are talking about a scenario where a geologist uses a scale to weigh two rocks together, with a total weight of 2 1/2 lbs, and rock 'a' is specified to be 1/7 of this total weight. To determine the weight of rock 'a', we simply divide the total weight by 7.

So, 2 1/2 lbs is equivalent to 2.5 lbs (since 1/2 is the same as 0.5). To find the weight of rock 'a', we take this total weight and perform the operation: 2.5 ÷ 7 = 0.357 lbs.

Therefore, rock 'a' weighs approximately 0.357 lbs. Remember, this is an estimation because the weight of the rock is being given as a fraction of the total weight, and actual weights can vary based on factors such as density and volume.

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the circle with center (3,5) and radius 2 has a equation?

Answers

[tex]\bf \textit{equation of a circle}\\\\ (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 \qquad \begin{array}{lllll} center\ (&{{ h}},&{{ k}})\qquad radius=&{{ r}}\\ &3&5&2 \end{array} \\\\\\ (x-3)^2+(y-5)^2=2^2\implies (x-3)^2+(y-5)^2=4[/tex]

What is the volume of a paperback book 21 cm tall, 12 cm wide, and 3.5 cm thick?

Answers

A book can be considered a rectangular prism. In order to find the volume of a rectangular prism, the width must be multiplied by the height and length. As a result we multiply 21cm x 12cm x 3.5 cm to get a volume of 882cm^2.

The volume of a cuboid is given as length × width × height thus the volume of the paperback book will be 882 cm².

What is volume?

Volume is the scalar quantity of any object that specified occupied space in 3D.

Volume has units of cube example meter³,cm³, etc.

Given a paperback book shape as cuboid

Length(tall) = 21 cm

Width(wide) = 12cm

Height (thick) = 3.5 cm

The volume of the cuboid is given as

Volume = length × height × width.

Volume = 21 × 12 × 3.5

Volume = 882 cm²

Hence" The volume of a cuboid is given as length × width × height thus the volume of the paperback book will be 882 cm²".

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For what values of a and b is the line 2x + y = b tangent to the parabola y = ax2 when x = 2?

Answers

Didn't you mean y = ax^2? "^" denotes "exponentiation."

The first derivative of y = ax^2 represents the slope of the tangent line to the curve of y = ax^2. Here, dy/dx = 2ax. When x = 2, dy/dx = 2a(2) = 4a.

The point of tangency is (2,y), where y = a(2)^2, or y=4a; thus, the point of tangency is (2,4a). The equation of the tangent line to y=ax^2 at (2,4a) is found by (1) differentiating y=ax^2 with respect to x, (2) letting x = 2 in the result: dy/dx = 2ax => dy/dx (at 2,4a) = 2a(2) = 4a

The line 2x + y = b is supposed to be tangent to y = ax^2 at (2,4a).

The slope of 2x + y = b is found by solving 2x + y = b for y:

y = b - 2x => slope m = -2

Thus, dy/dx = 4a = - 2, and thus a = -2/4, or a = -1/2. All we have to do now is to find the value of b. We know that 2x + y = b, so if x=-2 and y=-8,

2(-2) + [-8] = b = -4 - 8 = -12

Thus, the equation of the parabola is y = ax^2 = (-1/2)x^2.

a = -2 and b = -8 are the required a and b values.

The equation of the parabola is y = ax² = (-1/2)x² where a = -2 and b = -8 are the required values of a and b.

What is the slope of the tangent line?

The first derivative of y = ax² that represents the slope of the tangent line to the curve of y = ax² .

Here, dy/dx = 2ax.

When x = 2,

dy/dx = 2a(2) = 4a.

The point of tangency is (2,y), where y = a(2)², or y=4a;

thus, the point of tangency is; (2, 4a).

The equation of the tangent line to y=ax² at (2,4a)

Now differentiating y=ax² with respect to x,

dy/dx = 2ax

dy/dx (at 2,4a) = 2a(2) = 4a

The line 2x + y = b is tangent to y = ax² at (2,4a).

The slope of 2x + y = b can be found by solving 2x + y = b for y:

y = b - 2x

Slope m = -2

Thus, dy/dx = 4a = - 2, and thus a = -2/4, or a = -1/2. All we have to do now is to find the value of b.

We know that 2x + y = b, then if x=-2 and y=-8,

2(-2) + [-8] = b = -4 - 8 = -12

Thus, the equation of the parabola is y = ax² = (-1/2)x² where a = -2 and b = -8 are the required values of a and b.

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there are 1,525 pages in a book. Julia and Kim round the number of pages to the nearest hundred

Answers

1,525
In the case of rounding up, the number beside the must be above 5
But, in the case of rounding down, the number beside must be below 5.
The hundred place is the number 5.
The number before the 5 is the number 2
Since 2 is lower than 5, we round it down..
Thus the answer is 1,500

Hope this helps :))

Julia and Kim round the number of pages to the nearest hundred as 1500.

Given that, there are 1,525 pages in a book.

What is the rounding off numbers?

Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.

In the given number, digit in the tens place is 2, so the number rounded to nearest hundred as 1500.

Therefore, Julia and Kim round the number of pages to the nearest hundred as 1500.

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8 = 4x + 12 what does x equal

Answers

x = -1. 8 = 4x+12
-4 = 4x
-1 = x

8 = 4x + 12
1) subtract 12 from both sides.
-4 = 4x
2) divide each side by 4
-1 = x

What is the common difference for the arithmetic sequence?

4.7, 6, 7.3, 8.6, 9.9,...

Answers

The common difference is 1.3

It would be 1.3 like the other person said because 6-4.7 is 1.3 and 7.3-6 is 1.3 so that would be the sequence ( Explanation )

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