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neonofarm [45]
3 years ago
14

What is the equation of the quadratic graph with a focus of (3, 1) and a directrix of y = 5?

Mathematics
1 answer:
lbvjy [14]3 years ago
4 0

Answer:

The equation of the quadratic graph is f(x)= - (1/8) (x-3)^2 + 3 (second option)

Step-by-step explanation:

Focus: F=(3,1)=(xf, yf)→xf=3, yf=1

Directrix: y=5 (horizontal line), then the axis of the parabola is vertical, and the equation has the form:

f(x)=[1 / (4p)] (x-h)^2+k

where Vertex: V=(h,k)

The directix y=5 must intercept the axis of the parabola at the point (3,5), and the vertex is the midpoint between this point and the focus:

Vertex is the midpoint between (3,5) and (3,1):

h=(3+3)/2→h=6/2→h=3

k=(5+1)/2→k=6/2→k=3

Vertex: V=(h,k)→V=(3,3)

p=yf-k→p=1-3→p=-2

Replacing the values in the equation:

f(x)= [ 1 / (4(-2)) ] (x-3)^2 + 3

f(x)=[ 1 / (-8) ] (x-3)^2 + 3

f(x)= - (1/8) (x-3)^2 + 3

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marusya05 [52]
The answer would be 7.225.
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3 years ago
Read 2 more answers
Help please !! Thank u
leonid [27]

Answer:

parallel = same slope (-2x)

so it's y=-2x + b

let's find b by plugging in 1 for x and 3 for y (the coordinates)

3 = -2*1 + b

3 = -2 + b

5 = b

there you have it:

y = -2x +5

brainliest would really be appropriated (possible when someone else also leaves an answer)

4 0
3 years ago
1-sin60÷cos60=1-Tan30÷1+Tan30
ipn [44]

Step-by-step explanation:

LHS=(1-sin60)/cos60

=(1-√3÷2)/1÷2

=2(1-√3÷2)

=2-√3

RHS=(1-tan30)/(1+tan30)

={1-(1÷√3)}/{1+(1÷√3)}

={(√3-1)/√3}/{(√3+1)/√3}

=(√3-1)/(√3+1)

={(√3-1)(√3-1)}/{(√3+1)(√3-1)}

=(3-√3-√3+1)/(3-1)

=(4-2√3)/2

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Therefore LHS=RHS

8 0
3 years ago
QUESTION IS DOW BELOW 30 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP
ivann1987 [24]

The required solution is ∠RQT =  202°  and ∠QTS = 51°

<h3 />

<h3>What is a cyclic quadrilateral?</h3>

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It is also called as inscribed quadrilateral.

Its main property is that the sum of opposite angles of inscribed quadrilateral is always 180 degrees.

Now, the given circle has a cyclic quadrilateral QRST in which it is given that  ∠RQT =  202° and ∠QRS = 129°

Since,sum of the opposite angles of a cyclic quadrilateral =  180°  

⇒∠QTS + ∠QRS = 180°

⇒ ∠QTS  + ∠129° = 180°

⇒ ∠QTS = 180° - ∠129°

⇒ ∠QTS = 51°

Hence,the requires angles are ∠RQT =  202° and ∠QTS = 51°.

More about cyclic quadrilateral :

brainly.com/question/14323008

#SPJ1

5 0
2 years ago
Lara has $1,425 in her bank account. Write and solve an equation to show how much money she started with if that amount reflects
bixtya [17]
1,425 = 114%
so
1,425 = 114% • x


1,425 × 100 ÷ 114 = x
x = 1250

hope this helps!
8 0
3 years ago
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