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
Factor 2x^2 - 6x + 4 completely
katovenus [111]

Answer:

Step-by-step explanation:

Factor

2

out of

2

x

2

.

2

(

x

2

)

+

6

x

−

4

Factor

2

out of

6

x

.

2

(

x

2

)

+

2

(

3

x

)

−

4

Factor

2

out of

−

4

.

2

x

2

+

2

(

3

x

)

+

2

⋅

−

2

Factor

2

out of

2

x

2

+

2

(

3

x

)

.

2(

x

2

+

3

x

)

+

2

⋅

−

2

Factor

2

out of

2

(

x

2

+

3

x

)

+

2

⋅

−

2

.

2

(

x

2

+

3

x

−

2

)

6 0
3 years ago
Read 2 more answers
9.2 HW Central Angles, Arc Measures, & Arc Length
kap26 [50]

Answer:

I can help you with this, i just need the actual questions.

Step-by-step explanation:

5 0
3 years ago
Among 420 randomly selected employees at a company, the mean number of hours of overtime worked per month is 10 hours and the st
kari74 [83]

The margin of error of the random selection is 0.20

The given parameters are:

n = 420 --- the sample size

\sigma = 1.6 --- the standard deviation

\bar x = 10 --- the mean

\alpha = 99\% --- the confidence level.

The margin of error (E) is calculated as follows:

E = z \times \sqrt{\frac{\sigma^2}{n}}

So, we have:

E = z \times \sqrt{\frac{1.6^2}{420}}

E = z \times \sqrt{\frac{2.56}{420}}

The z-value for 99% confidence level is 2.576.

Substitute 2.576 for z

E = 2.576 \times \sqrt{\frac{2.56}{420}}

E = 2.576 \times \sqrt{0.006095}

Take square roots

E = 2.576 \times 0.0781

Multiply

E = 0.2012

Approximate

E = 0.20

Hence, the margin of error is 0.20

Read more about margin of error at:

brainly.com/question/14396648

8 0
2 years ago
Read 2 more answers
A piece of fabric is 2 yards long. The fabric is cut into 24 pieces of equal length.
Archy [21]
Each piece is 3 inches
6 0
3 years ago
Read 2 more answers
-8,-14,-20 whats the next term
Nookie1986 [14]
26 is the answer
because its counting by 6
8 0
2 years ago
Other questions:
  • Write a story or real life situation that situation that could be solved with 24 /6
    13·2 answers
  • Find the value of the x for the following 5x - 7 = 18
    11·2 answers
  • Please solve equations with elimination method, please!<br><br> y=-x^2-6x-10<br><br> y=3x^2+18x+22
    6·2 answers
  • if you make a scale drawing of a tree using the scake 5in =27ft uf the tree is 67.5 ft tall how tall is the scale drawing
    9·1 answer
  • When a number is decreased by 20% of itself, the result is 20. What is the number?
    10·1 answer
  • GUYS QUICK! what is the surface area of a sphere that has a radius of 5 cm
    15·2 answers
  • The sixth grade class went to a family fun center. out of the 154 students, 85 played laser tag. A total of 80 students roller s
    14·2 answers
  • Jenny will choose between two restaurants to purchase pizzas for her party. The first restaurant charges a delivery fee of $6 fo
    12·1 answer
  • The number of bacteria in a petri dish is 50,000 (on day 0) if the amount is doubling each day by when will the number of bacter
    7·1 answer
  • Answer this question!!!!!!!​
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!