Find the equation of a quadratic function in general form whose graph has points: (-2, 3) (0, 3) and (-4,-5).

Try your best to show complete work & explain your strategy.

Answers

Answer 1

Answer:

-x²-2x+3

Step-by-step explanation:

The first thing I noticed is that the first and second point has the same y intercept despite being only 2 x coordiantes away. This must mean that the vertex's x coordiante is probably (-1,4)

Because the vertex is probably (-1,4) the graph must also be concave down because the point (-4,-5) is below it

writing this in vertex form we get

-a(x+1)²+4

Where a is some constant

solve for a by plugging in (0,3)

3= -a(0+1)²+4

3= -a+4

-1= -a

a=1

therefore the equation looks like

-(x+1)²+4

expanding this so that it's in stantard form...

-(x²+x+x+1)+4

-x²-2x+3

which is the final answer


Related Questions

quall o numero de diagonais de um poligono com 15 lados

Answers

Answer:

90 diagonais.

Step-by-step explanation:

[tex]n(n-3)/2=15(15-3)/2=15*6=90[/tex]

4 + {−5 + [−3 + 4 + 2(−7 + 4) + 4] + 2}
7 + {−2 + [5 + 4(−3) + (−6 + 2) + (−3)]}
(−2) + {3 + [−4 + (3)] + 7} + (−5)
(−10) + {−7 + [−4 + 5(−9) + 5] + 8}
18 + 3{−4 + [−15 + 20 + (−3)] + (−9)}
−(−8 + 5) + {−4 + [−7 + (−9 − 5) + 3]}
− 9 + {−7 − 2[−(4 + 1) + (5 − 9)]} − 3
−1 − 3{6 − [4 + 2(−7 + 8) − 5] − 2}
−(−2) − {−(−7) + [−3 + (−5 − 2) + 6]}
−(−6 − 2) − 2{−4(−5) + 5[−3 + (−2)]}
6 − 2{−4 + 3[3 − 3(−8 − 5) + 14] − 7}
Me pueden ayudar por favor es urgente!!! y Buenas Noches ;)

Answers

Answer

it is 5 : )

Step-by-step explanation:

Jerry needs 216 posts to build a fence. He has 88 posts and needs P more. Write an equation that you could use to find the number of posts jerry still needs.

Answers

Answer:

P = 128 Post

Step-by-step explanation:

Total post needed = 216 posts

Number of post Jerry has = 88 posts

Number of posts jerry still needs = P

Total = Number of post Jerry has + Number of posts jerry still needs

216 = 88 + P

216 - 88 = P

128 = P

P = 128 Post

help me frll frll, my test is timed !!!! Which of the following scatterplots would have a trend line with a negative slope?
*y,
1
4.5
5 4
1.5
5.5
2.
4.25
3
25
5
2
3
3.75
1
3.5
3.5
1
2
3 4
5
35
425
Xy,
1
25
5
ا
1.5
3.5
4
2.
4.25
3
O
254 25
27

Answers

Answer:

i toke it on edu

Step-by-step explanation:

it is 2

Answer:

c

Step-by-step explanation:

Use two unit multipliers to convert 36 inches to miles.

Answers

Answer:

36 inches = 0.000568182 miles

Factorize (a+b)²-4ab​

Answers

Answer:

(a - b)²

Step-by-step explanation:

(a + b)² - 4ab

= a² + 2ab + b² - 4ab

= a² - 2ab + b²

= (a - b)²

What is 1/4 in feet?

Answers

Answer:

0.25 feet

7.62 centimeters

3 inches

Step-by-step explanation:

Not really a clear question-

Find y

Help me please

Answers

Answer:

y = 46

Step-by-step explanation:

Y=46 that’s the answer

solve in attachment....​

Answers

Answer:

2 ( Option A )

Step-by-step explanation:

The given integral to us is ,

[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]

Here 5 is a constant so it can come out . So that,

[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]

Now we can write √x as ,

[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]

Simplify ,

[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]

By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,

[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]

On simplifying we will get ,

[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]

Answer:

A)2

Step-by-step explanation:

we would like to integrate the following definite Integral:

[tex] \displaystyle \int_{0} ^{1} 5x \sqrt{x} dx[/tex]

use constant integration rule which yields:

[tex] \displaystyle 5\int_{0} ^{1} x \sqrt{x} dx[/tex]

notice that we can rewrite √x using Law of exponent therefore we obtain:

[tex] \displaystyle 5\int_{0} ^{1} x \cdot {x}^{1/2} dx[/tex]

once again use law of exponent which yields:

[tex] \displaystyle 5\int_{0} ^{1} {x}^{ \frac{3}{2} } dx[/tex]

use exponent integration rule which yields;

[tex] \displaystyle 5 \left( \frac{{x}^{ \frac{3}{2} + 1 } }{ \frac{3}{2} + 1} \right) \bigg| _{0} ^{1} [/tex]

simplify which yields:

[tex] \displaystyle 2 {x}^{2} \sqrt{x} \bigg| _{0} ^{1} [/tex]

recall fundamental theorem:

[tex] \displaystyle 2 ( {1}^{2}) (\sqrt{1} ) - 2( {0}^{2} )( \sqrt{0)} [/tex]

simplify:

[tex] \displaystyle 2 [/tex]

hence

our answer is A

Given the following geometric sequence, Find the common ratio (3, 18,108)

Answers

Answer:

6

Step-by-step explanation:

3*6=18

18*6=108

Given f(x) and g(x)= f(k•x), use the graph to determine the value of k

Answers

Answer:

[tex] \displaystyle \boxed{k = 3}[/tex]

Step-by-step explanation:

to determine the Value of k we need to find the equation of f(x) and g(x)

finding the equation of f(x):

f(x) is a linear function which form is given by:

[tex] \displaystyle f(x) =mx + b[/tex]

where:

m is the slope b is the y-intercept

from the graph we acquire that

[tex]b = 4[/tex]

to figure out m we can consider the following formula:

[tex] \displaystyle m = \frac{ \Delta y}{ \Delta x} [/tex]

from the graph we obtain that both ∆x and ∆y is 1 thus substitute:

[tex] \displaystyle m = \frac{ 1}{ 1} [/tex]

simplify:

[tex] \displaystyle m = 1[/tex]

altogether we acquire:

[tex] \displaystyle f(x) =x + 4[/tex]

finding the equation of g(x):

likewise f(x)

from the graph we obtain that

∆x=1∆y=3

thus substitute:

[tex] \displaystyle m = \frac{ 3}{ 1} [/tex]

simplify:

[tex] \displaystyle m = 3[/tex]

from the graph we acquire

b=4

altogether substitute therefore

[tex] \displaystyle g(x) =3x + 4[/tex]

finding the value of k:

given that,

[tex] \displaystyle \rm f(x) \: \text{and} \: g(x) =f(kx) = 3x + 4[/tex]

so our equation is

[tex] \displaystyle kx + 4 = 3x + 4[/tex]

cancel 4 from both sides:

[tex] \displaystyle kx = 3x [/tex]

divide both sides by x:

[tex] \displaystyle \boxed{k = 3}[/tex]

and we're done!

Disclaimer:

at the following link we posted the complete question

the complete question:

https://brainly.com/question/24201282

Answer:

k = 3

Step-by-step explanation:

Graph is in attachment .

Finding equation of first line [ f(x) ] :-

We can see that the line passea through point ( 0,4) . Therefore ,

y intercept = 4

Also it passes through (-4,0 )

Now let's find out slope .So that we can use the slope intercept form to find the equⁿ of the line.

m = y ₂ - y₁ / x ₂ - x₁ m = 4 - 0 / 0 - (-4) m = 4/4 m = 1

Equation of f(x) :-

y = mx + c y = 1 * x + 4 y = x + 4 f(x) = x + 4

Similarly when we will find the equⁿ of g(x) :-

y = 3x + 4g(x) = 3x + 4

By question :-

f(x ) and g(x) = f ( k • x ) 3x + 4 = kx + 4 kx = 3x k = 3

What is the domain and range of graph!!! 10 points!!!

Answers

Answer:

THIRD OPTION - Domain: (0, infinity)

Range: (-infinity, + infinity)

Step-by-step explanation:

The graph is an asymptote, therefore the domain must start at 0 and end at infinity. The range is all real numbers because eventually it will reach all y values.

the simplest rationalizing factor of
2√50?
PLEASE DO ANSWER THIS QUESTION CORRECTLY

Answers

Answer:

2/5√2

Step-by-step explanation:

2/√ 25 * 2

further:

ans (1/5)(√2)

Hi,

[tex]2\sqrt{50}\\\\=2\sqrt25*2}\\\\=2*5\sqrt{2}\\\\=10\sqrt{2}[/tex]

write two such ratios number whose multplicativen inverse is same as they are​

Answers

Answer:

1 and -1 are two rational numbers whose multiplicative inverse is same as they are.

Step-by-step explanation:

mark me brainlist

the first three terms of a series of which the nth term is 2n+1.​

Answers

Answer:

3, 5, 7

Step-by-step explanation:

Substitute n = 1, 2, 3 into the nth term rule

a₁ = 2(1) + 1 = 2 + 1 = 3

a₂ = 2(2) + 1 = 4 + 1 = 5

a₃ = 2(3) + 1 = 6 + 1 = 7

Answer:

3, 5, 7

Step-by-step explanation:

n = 1, 2, 3 into the nth term rule

a₁ = 2(1)+1=2+1=3

a2=2(2)+1=4+1=5

a3 = 2(3)+1=6+1=7

Can someone please help?

Answers

Answer:

f(x) = (x + 4)^2 - 5

Step-by-step explanation:

Parent function: f(x) = x^2

To show this in a way that may look more familiar, f(x) = 1(x - 0)^2 + 0

Vertex form: f(x) = a(x - h)^2 + k

We know a = 1, because the slope is the same as the parent function.

Vertex: (h,k)

We can see that the vertex of the graph is (-4, -5)

So h = -4 and k = -5

Now all we need to do is plug the variables into our equation.

f(x) = a(x - h)^2 + k

f(x) = 1(x + 4)^2 - 5

f(x) = (x + 4)^2 - 5

£410 is divided between Gordon, Malachy & Paul so that Gordon gets twice as much as Malachy, and Malachy gets three times as much as Paul. How much does Malachy get?

Answers

Answer:

malachy got 123 euros

Step-by-step explanation:

if i m right than give me brainliest

Stacy is building a candy house. She
worked on it 3 hours before lunch and
6 hours after lunch. How many total
hours did Stacy spend working on the
candy house?

Answers

Answer:

9 hours

Step-by-step explanation:

You have to add both hours to get the total amount. So 3+6=9

Answer:

9 hours

Step-by-step explanation:

Stacy worked on the house 9 hours because she worked 3 hours before lunch and 6 hours after lunch. 6+3=9

Which set of rational numbers is arranged from least to greatest? 1 over 5, −1.4, negative 1 over 2, 3

Answers

Answer:

[tex]-1.4, -\frac{1}{2}, \frac{1}{5}, 3[/tex]

Step-by-step explanation:

Given

[tex]\frac{1}{5}, -1.4, -\frac{1}{2}, 3[/tex]

Required

Order from least to greatest

We have:

[tex]\frac{1}{5}, -1.4, -\frac{1}{2}, 3[/tex]

Convert all fractions to decimal

[tex]0.2, -1.4, -0.5, 3[/tex]

Now order from least to greatest

[tex]-1.4, -0.5, 0.2, 3[/tex]

Replace fractions

[tex]-1.4, -\frac{1}{2}, \frac{1}{5}, 3[/tex]

The water level of a pond drops an inch every 12 days without rain. How
many days will it take the pond's water level to drop by 11 inches?

Answers

Answer:

1 to 7 days

Step-by-step explanation:

The sum of two numbers is 9 and their difference is 7. Find the two numbers.
8 and 1
4 and 5
6 and 3
9 and 0

Answers

Answer:

8 and 1

Step-by-step explanation:

? + ? = 9
? - ? = 7

8 + 1 = 9
8 - 1 = 7

Final Answer: 8 and 1

Have an amazing day!

Answer:

8 and 1

Step-by-step explanation:

The sum means that the two numbers added together make up what they're asking. Difference means you're subtracting between the two. For our purposes, we can just look at each answer option and firstly see which one has a difference of 7.

8-1=7

4-5=-1

6-3=3

9-0=0

And just to double check, we try adding 8 and 1, which is 9! Yay! :P

Find the measure of LM

Answers

It’s LM becuase look at the photo Lm means

Answer:

[tex]{ \tt{LM = ON}} \\ { \bf{6x - 7 = 2x + 9}} \\ { \bf{4x = 16}} \\ x = 4 \\ \\ { \bf{LM = 6(4) - 7}} \\ { \boxed{ \tt{LM = 17 \: units}}}[/tex]

The Banker's Rule is another type of simple interest computation that is similar to ordinary simple interest computation. It is based on a 360-day year, but you use the actual number of days in the term when calculating interest. Does this benefit the lender or the borrower? Explain.

Answers

Answer:

it would appear tp benefit the borrower. if interest (which is paid by the borrower) is computed on a 360 day year and there are 365 days in a year....

one could consider the "Bankers Rule" to give the borrower 5 "free" days of no interest paid

Step-by-step explanation:

How many odd numbers greater than 60000 can be formed, using numbers 2,3,4,5 and 6 if each digit is used only once in each number?​

Answers

Hello,

All the numbers must begin with  6.

There are still 2,3,4,5 digits :  4 possibilities.

4!=4*3*2*1=24

The first is 62345 and the last 65432.

simplyfy using appropiate properties 1/4×2/5+-1/6×3/2+3/7×2/5 ​

Answers

Answer:

-1/35

Step-by-step explanation:

* means multiply

because of pemdas you should do three multiplication parts first

(1/4×2/5)+(-1/6×3/2)+(3/7×2/5)

1/20 - 3/12 + 6/35

3/60 - 15/60 + 6/35

-12/60 + 6/35

-1/5 + 6/35

-7/35 + 6/35

-1/35

Answer:

3/140

Step-by-step explanation:

1/4 × 2/5 + (-1/6) × 3/2 + 3/7 × 2/5 ​=

= 2/20 - 3/12 + 6/35

**********************************************

We need the LCD of 20, 12, 35.

20 = 2^2 * 5

12 = 2^2 * 3

35 = 5 * 7

LCD = 2^2 * 3 * 5 * 7 = 420

**********************************************

= 42/420 - 105/420 + 72/420

= 9/420

= 3/140

A larger number is double the sum of 3 and a smaller number. The larger number is 2 less than 3 times the smaller
number. If y represents the larger number and x represents the smaller number, which equations model the situation?
Check all that apply.
Oy - 3x-2
3x-y = 2
3x-y=-2
y=2-3x
Oy=2(x+3)

Answers

Answer:

not sure what the O is there for?

if it is zero then Oy would make Oy=2(x+3) not correct

3x-y = 2

y=2(x+3)

Step-by-step explanation:

)

Which of the following is a composite number?
A. 1
B. 63
C.O
D. 19

Answers

B. 63

some simple googling would've been able to help you with this. but 0 isn't prime or composite, not sure about 1, 19 is prime, 63 is a definite composite

question is on the image.
can you do question a and b please
I'll you give the brainliest.

Answers

Answer:

a) i. 1/6

ii. 0

b) 1/6 * 60

=10

Answer:

[tex]a) 1)\frac{1}{6} \\ \\ 2)0 \\ \\b) \frac{1}{6} \times 60 = \frac{60}{6} = 10[/tex]

hope this helps you.

Surface area of a cuboid is 384
work out the volume

Answers

Answer:

is 512

Step-by-step explanation:

Help me solve for X I forgot how to this

Answers

Step-by-step explanation:

hope it helps you.........

Answer:

[tex]here \: is \: your \: solution : - \\ \\ here \: is \: a \: right \: traingle \: with \\ \\ base \: = 52 \: units \\ \\ hypotenuse \: = 65 \: units \\ \\ perpendicular \: = {?} \\ \\ we \: need \: to \: find \: perpendicular \\ \\ by \: using \: pythagorus \: theorem : - \\ \\ perpendicular ^{2} \: = base ^{2} + perpendicular ^{2} \: \\ \\ perpendicular^{2} \: = 65 {}^{2} - 52 {}^{2} \\ \\ perpendicular {}^{2} = (4225 - 2704) \\ \\ perpendicular {}^{2} = 1521 \\ \\ perpendicular = \sqrt{1521} \\ \\ perpendicular = 39 \: units \: \\ \\ hope \: it \: helps \: you \: [/tex]

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