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
According to the 2010 census The state with the fewest people is Wyoming with a population of 563,626. Write the number that is
KiRa [710]

Answer:

573,626

Step-by-step explanation:

563626 + 10000 = 573626

8 0
3 years ago
Please help I’ll give you brainliest!
Elodia [21]
Here is the answers for the first one

5 0
3 years ago
The diameter of a circle<br> Is 8 inches . What is the area ?
Elena L [17]

Answer:

radius=d/2 = 8/2 = 4inch.

Step-by-step explanation:

area = πr²

16π(inch)². or 352/7 (inch)².

hope this helps you.

8 0
2 years ago
Read 2 more answers
Which number is not a solution to the inequality below? x&lt;15 A -6 B -2 C 11 D 17 Please help! Thanks
Svetach [21]

Answer:

D.17

Step-by-step explanation:

We are given that inequality

x<15

We have to find the number which is not a solution of the given inequality.

x<15

It means the values of x which is less than 15.

A.-6

-6<15

Therefore, it is the solution of given inequality.

B.-2

-2<15

Therefore, it is the solution of given inequality.

C.11

11<15

Therefore, it is the solution of given inequality.

D.17

17>15

Therefore, it is not a solution of given inequality.

Option D is true.

6 0
2 years ago
A line includes the points 2, 10 and 0, 2 what is its equation in slope intercept form ​
IRINA_888 [86]

Answer:

y = -4x + 2

Step-by-step explanation:

y = mx + b ( slope-intercept)

1. Find Slope:

\frac{y^2 - y^1}{x^2 - x^1}

Lets name 2 as y2 and 10 as y1. And 0 as x2 and 2 as x1.

\frac{2-10}{0-2}  =  \frac{-8}{2} = -4

m/slope = -4

2. Find y-intercept:

y = mx +b

2 = -4(0) + b

= 2 = b

Y-intercept/b = 2

3. Put into slope-intercept form:

y = mx + b

= y = -4x + 2

Hope that helps! :D

4 0
3 years ago
Other questions:
  • Keian eats 1 and 1 half apples each day. What equation can be used to find b, the number of apples he will eat in 8 days?
    11·1 answer
  • Please help me please!!!!!
    15·1 answer
  • les had $26.00 when he went to the box city market to buy some fresh fruits and vegetables .when he left he had $11.70. how much
    7·2 answers
  • Find the value of n in the equation 6.2n- 3.7= 85+45
    7·1 answer
  • There is 1/2 gallon of fruit punch that will be shared equally among 5 friends. What fraction of a gallon of punch will each fri
    8·2 answers
  • What is 2x^2+x-3=0 factored
    12·1 answer
  • Alexa ran 22.5 miles less than Anthony last week. She ran a total
    8·1 answer
  • Hello anybody want to talk
    9·1 answer
  • Un numero aumentado en 5<br>​
    8·1 answer
  • Find the future amount at the end of four years for a $3000 investment that earns 5% at the end of each year
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!