1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
balandron [24]
3 years ago
11

What is the equation of the quadratic graph with a focus of (−4, −five fourths) and a directrix of y = twenty seven fourths?

Mathematics
2 answers:
MariettaO [177]3 years ago
4 0

Answer:

To find the quadratic equation:

Assume any point (x, y) on parabola.

Use the distance formula i.e, \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}

Distance between (x , y) and focus (-4 , \frac{-5}{4}) is:

\sqrt{(x+4)^2 +(y+\frac{5}{4})^2 }

Now, the distance between (x, y) and directrix of y = \frac{27}{4} is:

\sqrt{(y-\frac{27}{4})^2 }

On the parabola these distance are same;

\sqrt{(x+4)^2 +(y+\frac{5}{4})^2 } = \sqrt{(y-\frac{27}{4})^2 }

(x+4)^2 + (y+\frac{5}{4})^2 = (y-\frac{27}{4})^2

(x+4)^2 + y^2+\frac{25}{16}+\frac{5}{2}y = y^2+\frac{729}{16}-\frac{27}{2}y

or

(x+4)^2 = y^2+\frac{729}{16}-\frac{27}{2}y -y^2-\frac{25}{16}-\frac{5}{2}y

Simplify:

(x+4)^2 = \frac{729-25}{16}-\frac{27+5}{2}y

(x+4)^2 = \frac{704}{16}-\frac{32}{2}y

Simplify:

(x+4)^2 =44-16y  

or

16y = -(x+4)^2+44

Divide both sides by 16 we get;

y = \frac{-1}{16}(x+4)^2 + \frac{44}{16}

y = \frac{-1}{16}(x^2+16+8x) + \frac{11}{4}

or

y= \frac{-1}{16}x^2-1-\frac{1}{2}x+ \frac{11}{4}

Simplify:

y= \frac{-1}{16}x^2-\frac{1}{2}x+ \frac{7}{4}

therefore, the equation of the quadratic is; f(x) =negative one sixteenthsx^2 − one half x + seven-fourths.


horrorfan [7]3 years ago
4 0
<span> f(x) =negative one sixteenthsx2 − one half x +seven-fourths  </span>
You might be interested in
Who weighed more at the beginning of the show? *
Jobisdone [24]

Answer:

We need more information to answer this question, I'd gladly help if there was some more data.

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
If you sleep for 9 h one night, what fractional part of a day did you spend sleeping?
Angelina_Jolie [31]

Answer:

3/8 of the day

Step-by-step explanation:

A day is 24 hours

You spend 9 of them sleeping

The fraction you spend sleeping is

9/24

You can simplify the fraction by dividing the top and bottom by 3

9/3 = 3

24/3 = 8

3/8

7 0
3 years ago
Which experimental design compares two groups (randomly formed) on the same task, such as movement speed
anygoal [31]

Between-group design compares two groups (randomly formed) on the same task, such as movement speed.

Given things that there are two groups that are randomly formed for the same task.

A between-group design in experimental design is an experiment in which two or more groups of individuals are assessed simultaneously by separate testing factors. This design is typically used instead of, or in conjunction with, the within-subject design, which applies identical modifications of circumstances to each participant in order to monitor the reactions.

Learn more about experimental designs at brainly.com/question/17280313

#SPJ4

3 0
2 years ago
Find the volume of the solid. Round your answer to the nearest tenth
insens350 [35]

Answer:

Solution given:

Volume of cone=⅓πr²h

Volume of cylinder=πr²h

1.

volume =πr²h=π*(10/2)²*6=<u>471.23mm³</u>

2.

Volume =πr²h=π*8*12.5=<u>314.16in³</u>

3.

volume =⅓πr²h=⅓*π*4²*3=<u>5</u><u>0</u><u>.</u><u>2</u><u>6</u><u>c</u><u>m</u><u>³</u>

4.

Volume =⅓πr²h=⅓*π*(8/2)²*12=<u>2</u><u>0</u><u>1</u><u>.</u><u>0</u><u>6</u><u>i</u><u>n</u><u>³</u>

5 0
3 years ago
what is the equation in point slope form of a line that passes through the point (–8,2) and has a slope of 1/2?
madam [21]
Y=1/2x+6

Y-2=1/2(x+8)
Then simplify and get y by itself
5 0
3 years ago
Other questions:
  • A class has 16 boys and 24 girls.Of the 16 boys ,3 are left handed.Of the 24 girls, 2 are left handed.If a student is chosen at
    8·2 answers
  • Katelyn plans to apply for a $10,000 loan at an interest rate of 5.6% for 5 years. Use the monthly payment formula to complete t
    6·1 answer
  • In division what goes inside the house
    13·2 answers
  • Choose the problem with the same relationship that is modeled by the graph
    8·1 answer
  • Boat A and Boat B are racing across a bay. Boat A is 6 miles ahead of Boat B. Boat A has a top speed of 36 miles per hour, but B
    9·1 answer
  • PLEASE ANSWER QUICKLY!!!
    14·1 answer
  • What is the rational number equivalent to 3 point 12 with a bar over 12?
    8·2 answers
  • According to the graph, the __________________ is 57-43.
    11·1 answer
  • Work out the value of six squared plus three cubed
    11·1 answer
  • Show three ways to write the expression 5 times x algebraically.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!