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
4 times a certain number is 92. what is the number?
Zolol [24]

Answer: 23

Step-by-step explanation:

6 0
3 years ago
17, 18, 22, 31, 47 what is the next number
pogonyaev

Answer:

the next number is 47+ 16 =63

4 0
2 years ago
Please help!!! 10 points up!
Dimas [21]

Statements are all TRUE

sinA = \frac{a}{c} and cosB = \frac{a}{c}


cscA = 1/sinA = 1/(a/c) = \frac{c}{a} and secB = 1/cosB = 1/(a/c) = \frac{c}{a}

tanA = \frac{a}{b} and cotB= 1/tanB = 1/ (b/a) = \frac{a}{b}


8 0
3 years ago
Which graphs below represent an exponential function? Select all that apply.
Troyanec [42]
The two graphs in the second picture are the graphs of exponential functions. You can detect it from the L shaped graphs. 

The very first graph represents a linear function. A straight line always represents a linear function. In a Linear function, the change in the values of y is constant throughout in relative to change in x values.

The final graph represents a quadratic function rising on both ends. 

Therefore, option b and c are the correct answers
8 0
3 years ago
Read 2 more answers
kylie is 6 years younger than her brother. The sum of their ages is 22. How old is Kylie? How old is her brother
Nat2105 [25]
Kylie is 8 and her Brother is 14
14-6 = 8 * Kylie’s age is 8
Sum: 8 + 14 = 22
5 0
3 years ago
Other questions:
  • Jemma wants to teach her son to say thank you, jemma praises him and gives him a hug. Which reinforcement schedule is this?
    5·1 answer
  • Simplify the ratio 24/36
    7·2 answers
  • Can someone help with this please and thank you
    13·2 answers
  • 6 honeycrisp apples cost $1.99. How much do 11 apples cost?
    5·1 answer
  • Please help me ASAP because if I don’t finish it I’ll get in trouble
    14·2 answers
  • clay costs $5.60 per kilogram. The art teacher needs to buy 4.5 kilograms for the next project. How much will 4.5 kilograms of c
    15·2 answers
  • How to solve b 2 + 5b -35 = 3b
    6·1 answer
  • Look at the photo to see the question. if you can pls help!!
    13·1 answer
  • Put the following equation of a line into slope-intercept form, simplifying all
    5·1 answer
  • if n is an integer, what is the sum of the next three consecutive even integers greater than 2n? a. 6n + 12 b. 6n + 10 c. 6n + 4
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!