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
IRISSAK [1]
3 years ago
15

PLs help 50 PTS!!!!! PLEASE ILL GIVE BRAINLIEST!!!!!

Mathematics
1 answer:
Nookie1986 [14]3 years ago
3 0

Answer:

\large\boxed{y=\dfrac{1}{4}x^2-x-4}

Step-by-step explanation:

The equation of a parabola in vertex form:

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

<em>(h, k)</em><em> - vertex</em>

The focus is

\left(h,\ k+\dfrac{1}{4a}\right)

We have the vertex (2, -5) and the focus (2, -4).

Calculate the value of <em>a</em> using k+\dfrac{1}{4a}

<em>k = -5</em>

-5+\dfrac{1}{4a}=-4        <em>add 5 to both sides</em>

\dfrac{1}{4a}=1           <em>multiply both sides by 4</em>

4\!\!\!\!\diagup^1\cdot\dfrac{1}{4\!\!\!\!\diagup_1a}=4

\dfrac{1}{a}=4\to a=\dfrac{1}{4}

Substitute

a=\dfrac{1}{4},\ h=2,\ k=-5

to the vertex form of an equation of a parabola:

y=\dfrac{1}{4}(x-2)^2-5

The standard form:

y=ax^2+bx+c

Convert using

(a-b)^2=a^2-2ab+b^2

y=\dfrac{1}{4}(x^2-2(x)(2)+2^2)-5\\\\y=\dfrac{1}{4}(x^2-4x+4)-5

<em>use the distributive property: a(b+c)=ab+ac</em>

y=\left(\dfrac{1}{4}\right)(x^2)+\left(\dfrac{1}{4}\right)(-4x)+\left(\dfrac{1}{4}\right)(4)-5\\\\y=\dfrac{1}{4}x^2-x+1-5\\\\y=\dfrac{1}{4}x^2-x-4

You might be interested in
Which is more 10,000 ft or 2 miles
Trava [24]

Answer:

2 mi =10560ft

3 0
3 years ago
Read 2 more answers
In a market research survey of 29012901 ​motorists, 255255 said that they made an obscene gesture in the previous month. complet
harina [27]
A. 1-255255/29012901=0.991202017 is the probability of not making an obscene gesture.
b. The probability of none of 5050 making an obscene gesture is (a) raised to the power of 5050: 4.1591E-20 approx. We have not used the 5% rule in this binomial distribution.
8 0
3 years ago
Write a function using function notation to describe each situation. Find a reasonable domain and range for each function.
sergejj [24]
F(t)= 7.00 x t + 55 A reasonable domain is (0,1,2,3). The range is ($55,$62,$69,$76)
5 0
3 years ago
What is the y-intercept, b, of the additive relationship represented by this table?
mina [271]

Answer:

  • b = 3

Step-by-step explanation:

Use the table to find the slope and y-intercept

<u>Find the slope:</u>

  • m = (6 - 4)/(3 - 1) = 2/2 = 1

<u>Find b using the pair (1, 4):</u>

  • 4 = 1*1 + b
  • b = 4 - 1
  • b = 3

<u>The line is:</u>

  • y = x + 3

The y-intercept is 3

8 0
3 years ago
Read 2 more answers
X+5=121 please help me thank you. brainliest if helped
vampirchik [111]

Solution, solve\:for\:x,\:x+5=121\quad :\quad x=116

Steps:

x+5=121

\mathrm{Subtract\:}5\mathrm{\:from\:both\:sides},\\x+5-5=121-5

\mathrm{Simplify},\\x=116

\mathrm{The\:Correct\:Answer\:is\:x=116}

\mathrm{Hope\:This\:Helps!!!}

\mathrm{-Austint1414}

5 0
3 years ago
Other questions:
  • There are two water tanks, Tank #1 fills into Tank #2.
    6·1 answer
  • Find the solution to -x + 5 = -3.
    8·2 answers
  • 8 biscuits cost 24p altogether.How much do 5 biscuits cost?
    14·2 answers
  • Can u show me some division fractions
    7·1 answer
  • What is the equation of the line that passes through the point (-6,-7)(−6,−7) and has a slope of 0?
    8·2 answers
  • The number of calls that the employees in a call center took on Wednesday were recorded and combined in the histogram below.
    15·2 answers
  • I need how with plz
    9·2 answers
  • True or False question
    7·1 answer
  • Pls help and no unnecessary typin* I will report
    12·1 answer
  • On Monday there are 25 pencils in a basket, If 3 pencils are taken out of the basket each day, how many pencils are left in the
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!