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
maks197457 [2]
3 years ago
11

50 Points Please show graph

Mathematics
1 answer:
worty [1.4K]3 years ago
5 0

Answer:

The solutions are x = -9 , x = -5

Step-by-step explanation:

* Lets find the vertex of the parabola

- In the quadratic equation y = ax² + bx + c, the vertex of the parabola

 is (h , k), where h = -b/2a and k = f(h)

∵ The equation is y = x² + 14x + 45

∴ a = 1 , b = 14 , c = 45

∵ h = -b/2a

∴ h = -14/2(1) = -14/2 = -7

∴ The x-coordinate of the vertex of the parabola is -7

- Lets find k

∵ k = f(h)

∵ h = -7

- Substitute x by -7 in the equation

∴ k = (-7)² + 14(-7) + 45 = 49 - 98 + 45 = -4

∴ The y-coordinate of the vertex point is -4

∴ The vertex of the parabola is (-7 , -4)

- Plot the point on the graph and then find two points before it and

 another two points after it

- Let x = -9 , -8 and -6 , -5

∵ x = -9

∴ y = (-9)² + 14(-9) + 45 = 81 - 126 + 45 = 0

- Plot the point (-9 , 0)

∵ x = -8

∴ y = (-8)² + 14(-8) + 45 = 64 - 112 + 45 = -3

- Plot the point (-8 , -3)

∵ x = -6

∴ y = (-6)² + 14(-6) + 45 = 36 - 84 + 45 = -3

- Plot the point (-6 , -3)

∵ x = -5

∴ y = (-5)² + 14(-5) + 45 = 25 - 70 + 45 = 0

- Plot the point (-5 , 0)

* To solve the equation x² + 14x + 45 = 0 means find the value of

  x when y = 0

- The solution of the equation x² + 14x + 45 = 0 are the x-coordinates

 of the intersection points of the parabola with the x-axis

∵ The parabola intersects the x-axis at points (-9 , 0) and (-5 , 0)

∴ The solutions of the equation are x = -9 and x = -5

* The solutions are x = -9 , x = -5

You might be interested in
3 inches to the nearest 1/2 inch
DaniilM [7]

Answer:

6

Step-by-step explanation:

8 0
3 years ago
Name the figure below in two different ways.
Reil [10]

Answer: MUV OR VUM

Step-by-step explanation:

It is a line so anyway you name it is fine as lomg as its in it's respected order.

5 0
2 years ago
Read 2 more answers
T is the midpoint of AE. AT=4x-3 and TE= 2x+7, find the length of AE
iris [78.8K]

If T is the midpoint, then that means its exactly 1/2 of the way between 2 points

this means we can set the 2 given values equal

4x - 3 = 2x + 7

first move like terms to the same side

2x = 10

x = 5

now that we know the length of x, we plug it back in to get the length

4x - 3 + 2x + 7 = 6x + 4

6(5) + 4 = 34

7 0
3 years ago
HELPP FAST!! Will mark brainliest
melomori [17]

Answer:

No

Step-by-step explanation:

Because it is not going up by the same amount everytime

3 0
3 years ago
A house wife forgot her bank'Atm pin'which is a four digit number,but luckily she remembered some hints on how to recall this 'p
Liono4ka [1.6K]

Answer:

4829

Step-by-step explanation:

If the first digit is half of the second, that means the second is 2 times the first

So let's solve this algebraically...

The first digit could be called <em>a</em>

The second digit would have to be 2 times a (2a)

We can call the 3rd digit b

Since the sum of the second and third digit is 10, the equation would be this..

2x + b = 10, which is the same as b = 10 - 2x

The fourth digit is this equation

2x + 1

So the four digits are...

x, 2x, 10-2x, 2x+1

They are all equal to 23, which means...

x + 2x + 10-2x + 2x +1 = 23

After simplifying...

3x + 11 = 23

3x = 23 - 11

Which means...

3x = 12, x = 4

After you plug all that back into the prior equation you should get

first digit = 4 second digit = 8 third digit = 2 fourth digit = 9

Thank me later :)

(or just mark brainliest)

6 0
3 years ago
Other questions:
  • F 9 is added to twice a number and this sum is multiplied by 4​, the result is the same as if the number is multiplied by 4 and
    13·1 answer
  • Andre received $60 for his birthday and put it in his piggy bank. Each week, he puts 3 more dollars in his bank. The amount of m
    10·1 answer
  • What is the following sum?<br> 4 sq root 5+2 sq root 5<br> will mark brainliest
    14·2 answers
  • Square of 9 less than a number is 3 less than the number
    11·2 answers
  • Point A is located at (-5, 8) and is translated 4 units up. What are the coordinates of point A'?
    12·2 answers
  • Whats 2+2 as a fraction
    15·2 answers
  • Na lanchonete da escola há um sanduíche muito pedido que custa R$ 6,00. Os donos estão estudando aumentar o preço desse sanduích
    12·1 answer
  • An ice-making machine needs to be switched on
    11·1 answer
  • The interest on a note of $32,000 at 9% for three months is
    11·1 answer
  • A garden table and a bench cost $1000 combined. The cost of the garden table is three times the cost of the bench. What is the c
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!