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
Likurg_2 [28]
3 years ago
15

Find the equation, (f(x) = a(x - h)2 + k), for a parabola containing point (2, -1) and having (4, -3) as a vertex. What is the s

tandard form of the equation?
Mathematics
1 answer:
Nataliya [291]3 years ago
6 0

Answer:

f(x)=\frac{1}{2}x^2-4x+5

Step-by-step explanation:

A parabola is written in the form

f(x)=a((x-h)^2+k) (1)

where:

h is the x-coordinate of the vertex of the parabola

ak is the y-coordinate of the vertex of the parabola

a is a scale factor

For the parabola in the problem, we know that the vertex has  coordinates (4,-3), so we have:

h=4 (2)

ak=-3

From this last equation, we get that a=\frac{-3}{k} (3)

Substituting (2) and (3) into (1) we get the new expression:

f(x)=-\frac{3}{k}((x-4)^2+k) = -\frac{3}{k}(x-4)^2 -3 (4)

We also know that the parabola  contains the point (2,-1), so we can substitute

x = 2

f(x) = -1

Into eq.(4) and find the value of k:

-1=-\frac{3}{k}(2-4)^2-3\\-1=-\frac{3}{k}\cdot 4 -3\\2=-\frac{12}{k}\\k=-\frac{12}{2}=-6

So we also get:

a=-\frac{3}{k}=-\frac{3}{-6}=\frac{1}{2}

So the equation of the parabola is:

f(x)=\frac{1}{2}((x-4)^2 -6) (5)

Now we want to rewrite it in the standard form, i.e. in the form

f(x)=ax^2+bx+c

To do that, we simply rewrite (5) expliciting the various terms, we find:

f(x)=\frac{1}{2}((x^2-8x+16)-6)=\frac{1}{2}(x^2-8x+10)=\frac{1}{2}x^2-4x+5

You might be interested in
Characteristics of Relations
eduard
Its not function at all
8 0
3 years ago
The city plan includes parks reopening with probability = 1/2, diners with 20% chance, and dental offices with probability = 0.3
e-lub [12.9K]

Answer:

Parks, then dental offices, and finally diners

Step-by-step explanation:

Parks = 50%

Diners = 20%

Dental offices = 30%

Order the place in order of decreasing probability.

If this answer is correct, please make me Brainliest!

5 0
3 years ago
Read 2 more answers
How many decimals in 1000
yarga [219]

Answer:

if your number is 1000 there should be one decimal at the end so it should be 1000. Because 1000. And 1000 are the same thing

Step-by-step explanation:

4 0
3 years ago
Find the distance between the points (–3, 2) and (0, 3).
Oksi-84 [34.3K]

Answer: \sqrt{10}\ units

Step-by-step explanation:

You need to use the following formula:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Given the points  (-3, 2) and (0, 3), you can identify that:

x_2=-3\\x_1=0\\\\y_2=2\\y_1=3

Then, the final step is to substitutes these coordinates into the formula.

So, the distance between the given points is:

d=\sqrt{(-3-0)^2+(2-3)^2}\\\\d=\sqrt{10}\ units

6 0
3 years ago
1 5/6 x 2 1/4 = <br> ANSWER ASAPPP . BE RIGHT AND EXPLAIN PLS
MariettaO [177]

Answer:

25

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • square GYTD has vertices G(-4,3), Y (0,3), T (0,-1) and D (-4, -1) square GYTD is translated 2 units left and 2 units up to prod
    12·1 answer
  • What is 29 fifths as a mixed number
    7·2 answers
  • PLZ HELP ASAP! Tysm!
    13·1 answer
  • Please help, 10 points
    12·1 answer
  • True or false. A triangle is a figure formed by three segments connecting collinear points
    9·2 answers
  • Find the length of side AC. <br> A) 5 3 <br> B) 5 2 <br> C) 10 2 <br> D) 5 2 2
    8·1 answer
  • Which are dependent events? Check all that apply
    12·2 answers
  • Question
    14·1 answer
  • Hi, I am trying to find the Area but I cant tell if its 2D or 3D help please!
    13·1 answer
  • 10 + 2 - 3 = 3(2 + 2)
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!