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
Nina [5.8K]
3 years ago
15

Find the quadratic function that has a vertex at (3,4) and goes through the point (0,13).​

Mathematics
1 answer:
vladimir2022 [97]3 years ago
4 0

Answer:

f

(

x

)

=

−

1

2

x

2

+

3

x

−

1

2

Explanation:

A quadratic function can be written in vertex form as:

f

(

x

)

=

a

(

x

−

h

)

2

+

k

where

(

h

,

k

)

is the vertex and

a

is a constant multiplier.

In our example the vertex

(

h

,

k

)

is

(

3

,

4

)

, so we can write:

f

(

x

)

=

a

(

x

−

3

)

2

+

4

Given that this passes through the point

(

1

,

2

)

, we must have:

2

=

a

(

1

−

3

)

2

+

4

=

4

a

+

4

Subtract

4

from both ends to get:

−

2

=

4

a

Divide both sides by

4

and transpose to find:

a

=

−

1

2

So our quadratic function can be written in vertex form as:

f

(

x

)

=

−

1

2

(

x

−

3

)

2

+

4

We can multiply this out and simplify as follows:

f

(

x

)

=

−

1

2

(

x

−

3

)

2

+

4

f

(

x

)

=

−

1

2

(

x

2

−

6

x

+

9

)

+

4

f

(

x

)

=

−

1

2

x

2

+

3

x

−

9

2

+

4

f

(

x

)

=

−

1

2

x

2

+

3

x

−

1

2

Step-by-step explanation:

PLZ MARK ME BRAINLYIST

You might be interested in
Round 69.625 to the nearest whole<br> number, the nearest tenth, and the<br> nearest hundredth.
muminat

70 to the nearest whole number

69.6 to the nearest tenth

69.63 to the nearest hundredth

BRAINLIEST PLSSS

6 0
1 year ago
Can you pls help? This is a multiple choice, and including the answer can u add a one sentence explanation on why? Tysm! I’ll gi
prohojiy [21]

Answer:

A and D

Step-by-step explanation:

5 0
2 years ago
Find the total area for the regular pyramid.
hram777 [196]

Answer:

  • Option B

Step-by-step explanation:

Given is the hexagonal pyramid.

We know the radius of the base is same as its side.

<u>Find the base area:</u>

  • A = 3√3/2a²
  • A = 3√3/2*6² = 54√3

<u>Given the height and radius, find the side of the lateral triangular faces:</u>

  • \sqrt{8^2+6^2} =\sqrt{100} =10

Each of 6 triangles have sides 10, 10 and 6 units.

<u>Find the area using heron's formula:</u>

  • s = P/2 = (10*2 + 6)/2 = 13
  • s - a = s - b = 13 - 10 = 3
  • s - c = 13 - 6 = 7
  • A = \sqrt{s(s-a)(s-b)(s-c)} =\sqrt{13*3*3*7} =3\sqrt{91}

<u>Total surface area:</u>

  • S = 6*3\sqrt{91}+54\sqrt{3}  =18\sqrt{91}+54\sqrt{3}

Correct choice is B

3 0
2 years ago
21 times 9 equals 9 times 21 what is the property
Reil [10]
Commutative property....
5 0
2 years ago
A ceramic vase that cost an antique store $5 was marked $20. What is the percentage markup on the price of the ceramic vase?
Anika [276]
The answer would be 75%%%%
8 0
3 years ago
Other questions:
  • Question: Michelle is making goodie bags for Christmas filled with chocolate and candy. Chocolates cost $2.50 per lb and candy c
    7·1 answer
  • Graph f(x) = 2 sin x.<br> Use 3.14 for T.
    7·1 answer
  • Six sandwiches are being divided evenly by 4 friends.how many sandwiches will each friend get.
    13·2 answers
  • Which of the following approaches is most suitable for auditing the finance and investment cycle?
    12·2 answers
  • Help me solve this equation!!<br><br> 5x + 3x = ? when x = 5
    8·2 answers
  • A sequence is defined by the formula f(n+1)=f(n)−3. If f(4)=22, what is f(1)?
    8·2 answers
  • Help me please !!!!!​
    7·1 answer
  • Clare has a recipe for yellow cake. She uses 9 ⅓ cups of flour to make 4 cakes. Noah will follow the same recipe. He will make c
    8·2 answers
  • The graph of which function has a y-intercept of 3?
    10·1 answer
  • A penny, nickel, and dime are simultaneously flipped. What is the probability that heads are showing on at least 6 cents worth o
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!