What is the equation of a parabola if the vertex is (1, 4) and the directrix is located at y = 7?

Answers

Answer 1

According to the vertex and the directrix of the given parabola, the equation is:

[tex]y = \frac{3}{4}(x - 1)^2 + 4[/tex]

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

[tex]y = a(x - h)^2 + k[/tex]

In which a is the leading coefficient.

The directrix is at y = k + 4a.

In this problem, the vertex is (1,4), hence:

[tex]h = 1, k = 4[/tex]

The directrix is at y = 7, hence:

[tex]4 + 4a = 7[/tex]

[tex]a = \frac{3}{4}[/tex]

Hence, the equation is:

[tex]y = a(x - h)^2 + k[/tex]

[tex]y = \frac{3}{4}(x - 1)^2 + 4[/tex]

More can be learned about the equation of a parabola at https://brainly.com/question/26144898


Related Questions

f(x)=2x−2

g(x) = −2x + 1

Find f(5) • g(3)

Answers

Answer:

-40

Step-by-step explanation:

(2(5) - 2) (-2(3) + 1)

(10 - 2) (-6 + 1)

8(-5)

-40

What is the length of the hypotenuse of the triangle when x=10​?

The length of the hypotenuse is about

Answers

Answer:

84 (nearest whole number)

Step-by-step explanation:

If x = 10,

Longest leg = (7 x 10) + 4 = 74

Shortest leg = 4 x 10 = 40

Using Pythagoras' Theorem a² + b² = c² (where a and b are the legs and c is the hypotenuse of a right triangle):

⇒ 74² + 40² = c²

⇒ 7076 = c²

⇒ c = √7076 = 84.11896...

⇒ hypotenuse = 84 (nearest whole number)

Answer:

84

Step-by-step explanation:

[tex] \sqrt{ {(40)}^{2} + {74}^{2} } = 84.1[/tex]

Can somone pls help me on this (:

Answers

Answer:

Step-by-step explanation:

When it comes to mathematical concepts, those tiny numeral superscripts called exponents can intimidate even the most earnest student. One thing that helps stop the anxiety is understanding the importance of exponents in everyday math applications.

5 real-life uses:

pH ScalesWriting Large or Small NumbersTaking MeasurementsRichter ScalesFinance

Please Help!
Amelia has 6/12 of sand in her bucket. Alex has 3/9 of sand in his bucket. Who has more and by how much??

Answers

Answer:

Amelia has more she has 1/2 and Alex has 1/3

what is the size of the smallest increment shown on a inch tape measure

Answers

Answer:

1/16″: There are 16 sixteenth inches in one inch. This is the smallest line you'll find on the ruler. Two sixteenth markings equal one eighth.

Step-by-step explanation:

Answer:

1/16″: There are 16 sixteenth inches in one inch. This is the smallest line you'll find on the ruler. Two sixteenth markings equal one eighth.

Step-by-step explanation:

A storage trunk is 40 inches wide by 28 inches deep by 36 inches high. What is the volume of the trunk?​

Answers

Answer:

40 x 28 x 36 = 40,320. Hope this helped

I do not know the answer for this, what is the answer?

Answers

Answer:

Reflection and then translation

Step-by-step explanation:

It is a reflection because it flips across and then a translation because it moves down. I hope this helps you.

Answer:

Reflection then translation.

Hope this helps!

Explain about Pythagorean Theorem in your own words.
Without looking it up.

Answers

Answer:

The Pythagorean theorem just talks about the connection  between the lengths of the sides of right triangles. Something like that i guess

Step-by-step explanation:

Given TT = 3.142 the volume of the r = 4cm and h=8cm,Find the volume of the cone.​

Answers

the volume of the cone.​

1/3 pi r^2h

Answer:

134.04

Step-by-step explanation:

Formula for Volume of a Cone = TT r^2 h/3

= 3.142 × 4^2 × 8/3

what is x in this problem simplify
x−15≤−6

Answers

Answer:

x-15[tex]\leq[/tex]-6  1. +15 on both sides

x  [tex]\leq[/tex]9

What Is the slope of a line perpendicular to y=x-6

Answers

The slope of a line that is perpendicular to y = x - 6 means that the slope has to be a negative reciprocal of the original slope

That means the slope of the line that is perpendicular to y = x - 6 is '-1'

Hope that helps!

Convert the following number to a percent 68/ 23 If needed, round to the nearest whole.​

Answers

Step-by-step explanation:

[tex] \frac{68}{23} [/tex]

[tex] = 2.956521739130434[/tex]

[tex] = 2.956521739130434 \times 100[/tex]

= 295.6521739130434%

=296%

Answer:

296%

Explanation:

→ 68/23

to turn it unto fraction, multiply it by 100

→ 68/23 * 100

simplify

→ 6800/23

divide the number

→ 295.65

final answer in percentage

→ 296%

I need EXTREME HELP PLEASE

Answers

Answer:

8 months

Step-by-step explanation:

194-3m = 217-6m

3m = 23

m=7.666666.....  (8 months

9=v+4/v+12

find the value of v

extra points to brainliest

Answers

Answer: v = -13

Step-by-step explanation:

Multiply both sides of the equation by (v+12). On the right side, the (v+12) terms will cancel leaving only (v+4). On the left, we will have 9(v+12). Therefore:

[tex]9(v+12)=v+4[/tex]

Distribute the 9 into the parenthesis to get:

[tex]9v+108=v+4[/tex]

Subtract 'v' on both sides to get:

[tex]8v+108=4[/tex]

Subtract 108 from both sides to get:

[tex]8v=-104[/tex]

Divide both sides by 8 to get:

[tex]v=-13[/tex]

Question 4 of 5
Find the volume of the figure.
7 cm
3 cm
5 cm
O A. 105 cm3
OB. 175 cm3
C. 63 cm3
O D. 315 cm3

Answers

Answer:

A

Step-by-step explanation:

because multiply the all the side and it will be 105

The answer is A. 105 cm3

3 x 5= 15
15 x 7 = 105

there are 200 students in the 8th grade. 40 students are taking art. What percentage of 8th graders at Euclid Middle School are taking art?

Answers

20 percent because 200 divided by 40 that’s five so we need a number that would times that to get 100 so five times 20 equals 100 percent the answer is 20 percent

Answer:

20%

Step-by-step explanation:

You find percentage through division, but this one is easier than most since percentages are always out of 100, so 200/2 and 40/2 means 40 is 20% of 200.

what is the sum of 5x - 6y + z and 5x - 6y - z

Answers

Answer:

solution,

5x-6y+z+5x-6y-z

(+z and -z will be cancelled)

now,

5x+5x-6y-6y

10x+ 12y( because 2 minus makes plus)

5x - 6y + x + 5x - 6y - z

Combine like terms:

5x - 6y + 1z + 5x - 6y - 1z (the ones’ are usually invisible)
10x - 12y (positive and negatives cancel out)

Final answer: 10x - 12y


Hope this helps!

Which of the following describes the graph?
A.
a relation only
B.
neither a function nor a relation
Which of the following describes the graph?
A.
a relation only
B.
neither a function nor a relation
C.
a function only
D.
both a relation and a function
C.
a function only
D.

Answers

C. function only if I am correct hope this helps

–2 x – 4 > –64 what is the answer to this problem

Answers

Answer:

x<30

Step-by-step explanation:

-2x-4> -64

add 4 to both sides

-2x-4+4> -64+4

simplify the arithmetic

-2x> -64+4

-2x>-60

divide both side by -2

When dividing or multiplying by a negative number, always flip the inequality sign

-2x/-2 <-60/-2

Cancel out the negatives:

2x/2<-60/-2

Simplify the fraction:

x<-60/-2

Cancel out the negatives:

x<60/2

Find the greatest common factor of the numerator and denominator:

x<30 . 2 / 1 . 2

Factor out and cancel the greatest common factor:

x<30

Answer: x<30

explanation: Hope this helps :)

For every 2 pages of a book that Bernice reads, Charmaine reads 3. When Charmaine
had 16 pages left, Bernice had 36. How many pages are there in the book?

Answers

Answer:

76

Step-by-step explanation:

Let x = number of pages

Since Charmaine had 16 pages left, subtract 16 from x to indicate that is the number of pages read like this: x - 16

Divide that by 3 like this: (x - 16)/3

Do the same for Bernice: (x - 36)/2

Make them equal to each other

(x - 16)/3 = (x - 36)/2

Cross multiply

2(x - 16) = 3(x - 36)

Distribute

2x - 32 = 3x - 108

Move like terms to the same side by subtracting 2x from both sides

2x - 32 = 3x - 108

- 2x         - 2x

-32 = x - 108

Add 108 to both sides

-32 = x - 108

+ 108    + 108

x = 76

This means there are 76 pages in the book.

10
30 (2.-4)
10
A. 5
B. 1
C. -1
D. -5

Answers

Answer:

A

Step-by-step explanation:

correct me if I'm wrong

answer then get brainliest :)​

Answers

Answer:

[tex] \frac{2}{5} = \frac{6}{15} = \frac{12}{45} [/tex]

Michelle bought five packs of crayons for $16.25 What is the cost of a pack of crayons, in dollars, if all the packs cost the same?

Answers

Answer:

Michelle bought a pack of crayon for $3.25

Step-by-step explanation:

Number of packs = 5

The cost of a pack of crayons =

(Cost of 5 packs of crayon) / (number of packs of crayons)

The cost of a pack of crayons = ($16.25 ) /  5

The cost of a pack of crayons = $3.25

find the point of intersection:
3x=y-2
6x=4-2y

Answers

Answer: (0, 2)

3x = y - 2
6x = 4 - 2y

3x = y - 2
- y - y
-y + 3x = - 2
- 3x - 3x
-y = - 3x - 2
/-1 /-1
y = 3x + 2


6x = 4 - 2y
+ 2y + 2y
2y + 6x = 4
- 6x - 6x
2y = - 6x + 4
/2 /2
y = -3x + 2


y = 3x + 2
y = -3x + 2


3x + 2 = -3x + 2
- 2 - 2
3x = -3x
/3 /3
x = 0


y = 3x + 2
y = 3(0) + 2
y = 2

(x, y) --> (0, 2)

Therefore, the two equations intersect at (0, 2)



Hope this helps!

Which equation will have the same solution as

3(2x - 1) + 4x = 13?

A 10x = 14
B. 9x = 14
C. 10x = 16
D. 9x = 16

Answers

Answer:

C. 10x=16

Step-by-step explanation:

3(2x-1)+4x=13

Distribute the 3 by multiplying it by 2x and -1.

6x-3+4x=13

Add same properties. 6x and 4x     6x+4x=10x

10x-3=13      

Add 3 to both side get rid of the negative 3     -3+3=0    13+3=16

10x=16

Answer:

C

Step-by-step explanation:

10x=16

what is the geometric mean of 10 and 24

Answers

Answer:

26

Step-by-step explanation:

you square both 10 and 24

you then will get 100 and 576

you then will add them together

and get 676

since 676 is not a whole number

you then will dive the number by 4

to get the numbers

13 and 4

13 [tex]\sqrt{4} \\[/tex]

13*2 because the square root of 4 is 2

13*2 =26

A bike store sells scooters at 45% markup. If the store sells each scooter for $87 then what is the original price?

Urgent with 12 pts.

Answers

132 I think it should be right

Sarah's brother is 12 less than twice her age. If Sarah is 16, what equation represents this situation?

Answers

The equation that can be used to represent the ages of Sarah and his brother will be 2x - 12 = 16.

How to solve the equation

From the question given, Sarah's brother is 12 less than twice her age and Sarah is 16.

Let Sarah's age be represented by x.

Therefore, the equation to represent the situation will be:

= (2 × x) - 12 = 16

2x - 12 = 16

2x = 16 + 12.

2x = 28

x = 28/2 = 14

Sarah is 14 years.

Learn more about equations on:

https://brainly.com/question/13763238

Which equation is equivalent to 10+2(x−1)+7x=3x+1?

Answers

Answer:

Answer is x = -7/6

Step-by-step explanation:

please look at the image

PQ is a straight line segment.According to the information marked in the figure, (I) Find the magnitude of PÔS. (ii) Find magnitude of SÔQ.



PLEASEEEEEEE HEELPPP!!
99 POINTS!! btw turn the attached picture upside down​

Answers

Answer:

magnitude of PÔS = 60°

magnitude of SÔQ = 120°

note: a straight line has always 180°

solve for x:

PÔS + SÔQ = 180°3x + 2x + 80° = 180°5x = 180° - 80°5x = 100°x  = 20°

m∠POS

3x 3(20°)60°

m∠SOQ

2x + 80°2(20°) + 80°40° + 80°120°

So to find angle POS and SOQ we have to find value of x first.

[tex] \\ [/tex]

[tex] \rm \angle POS + \angle SOR + \angle ROQ = 180 \degree \\ [/tex]

Reason:-

Sum of angles on same line.

By the way it can be any number of angles but they should meet at same point. And their sum is always 180°. Remember linear pair? It is also same aspect but there will be only two angles.

[tex] \\ [/tex]

So:-

[tex] \\ [/tex]

[tex] \dashrightarrow \sf \angle POS + \angle SOR + \angle ROQ = 180 \degree \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow \sf 3x + 2x+ 80= 180 \degree \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow \sf 5x+ 80= 180 \degree \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow \sf 5x= 180 - 80 \degree \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow \sf 5x= 100 \degree \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow \sf x= \dfrac{100}{5} \degree \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow \sf x= \dfrac{5 \times 20}{5} \degree \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow \sf x= \dfrac{\cancel5 \times 20}{\cancel5} \degree \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow \sf x= \dfrac{1 \times 20}{1} \degree \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow \bf x=20\degree \\ [/tex]

[tex] \\ \\ [/tex]

Verification:-

[tex] \\ [/tex]

[tex] \dashrightarrow \sf 3x + 2x+ 80= 180 \degree \\ [/tex]

Put value of x

[tex] \\ [/tex]

[tex] \dashrightarrow \sf( 3 \times 20) + (2 \times 20)+ 80= 180 \degree \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow \sf60 + (2 \times 20)+ 80= 180 \degree \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow \sf60 + 40+ 80= 180 \degree \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow \sf100+ 80= 180 \degree \\ [/tex]

[tex] \\ [/tex]

[tex] \dashrightarrow \bf180= 180 \degree \\ [/tex]

LHS = RHS

HENCE VERIFIED!

[tex] \\ [/tex]

Angle POS = 3xAngle POS = 3 × 20Angle POS = 60°

Angle SOQ = 2x + 80Angle ROQ = 2 × 20 + 80Angle ROQ = 40 + 80Angle ROQ = 120°
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