![klk597703](/avatars/10370.jpg)
klk597703
30.06.2019 •
Mathematics
What is the equation of the quadratic graph with a focus of (3, 1) and a directrix of y = 5? f(x) = one eighth (x − 3)2 + 3 f(x) = −one eighth (x − 3)2 + 3 f(x) = one eighth (x − 3)2 − 3 f(x) = −one eighth (x − 3)2 − 3
Solved
Show answers
More tips
- L Leisure and Entertainment The Best Film of 2010: A Look Back at the Academy Awards...
- H Health and Medicine Simple and Effective: How to Get Rid of Cracked Heels...
- L Leisure and Entertainment What to Bring on a Hike? Essential Items to Pack for a Safe and Enjoyable Adventure...
- L Leisure and Entertainment Couchsurfing: A New Way to Travel...
- S Style and Beauty Autotanning: Harmful or Safe?...
- F Food and Cooking 10 Ideas for a Wedding Anniversary Gift...
- H Health and Medicine How to Reduce Sweating in the Heat and Beyond: Say Goodbye to Excessive Sweat...
- F Food and Cooking Do Aphrodisiacs Really Work? Separating Fact from Fiction...
- H Health and Medicine What to Eat to Lose Weight?...
- A Animals and plants How to Teach Your Parrot to Talk?...
Answers on questions: Mathematics
- M Mathematics The segments shown below could form a triangle....
- M Mathematics What is the linear inequality shown in the graph?...
- M Mathematics Cuales son los divisores de : divisores de 25 divisores de 28 divisores de 50...
- M Mathematics What is the difference of 9/10 and 2/3...
- M Mathematics When output increases, the PPC of the economy , indicating in the economy....
- M Mathematics After a discount of 5% the sales price of a game system is $106.78 what is the original price...
Ответ:
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
Ответ: