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
lesya [120]
1 year ago
8

Given the vertex of a quadratic function, find the axis of symmetry.

Mathematics
1 answer:
motikmotik1 year ago
5 0

(i) The equation of the axis of symmetry is x = - 5.

(ii) The coordinates of the vertex of the parabola are (h, k) = (4, - 18). The x-value of the vertex is 4.

(iii) According to the <em>vertex</em> form of the <em>quadratic</em> equation, the parabola opens down due to <em>negative</em> lead coefficient and has a vertex at (2, 4), which is a <em>maximum</em>.  

<h3>How to analyze and interpret quadratic functions</h3>

In this question we must find and infer characteristics from three cases of <em>quadratic</em> equations. (i) In this case we must find a formula of a axis of symmetry based on information about the vertex of the parabola. Such axis passes through the vertex. Hence, the equation of the axis of symmetry is x = - 5.

(ii) We need to transform the <em>quadratic</em> equation into its <em>vertex</em> form to determine the coordinates of the vertex by algebraic handling:

y = x² - 8 · x - 2

y + 18 = x² - 8 · x + 16

y + 18 = (x - 4)²

In a nutshell, the coordinates of the vertex of the parabola are (h, k) = (4, - 18). The x-value of the vertex is 4.

(iii) Now here we must apply a procedure similar to what was in used in part (ii):

y = - 2 · (x² - 4 · x + 2)

y - 4 = - 2 · (x² - 4 · x + 2) - 4

y - 4 = - 2 · (x² - 4 · x + 4)

y - 4 = - 2 · (x - 2)²

According to the <em>vertex</em> form of the <em>quadratic</em> equation, the parabola opens down due to <em>negative</em> lead coefficient and has a vertex at (2, 4), which is a <em>maximum</em>.  

To learn more on quadratic equations: brainly.com/question/1863222

#SPJ1

You might be interested in
What is the measure of the angle at the tail end of the kite?
Alja [10]

Answer:

79 inches if don't believe me dont

Step-by-step explanation:

just putting in words give me points so

6 0
3 years ago
How to solve all of this
photoshop1234 [79]
Start circle: πd = (3.14)(19) = 59.7

Move diagonally to the circle with the radius of 6.2.

Second circle: 2πr = 2(3.14)(6.2) = 39

Move upwards to the circle with the radius of 10.5

third circle: 2πr = 2(3.14)(10.5) = 66

Move right to the circle with the diameter of 16.6

Fourth circle: πd = (3.14)(16.6) = 52.2

Move down to the circle with the diameter of 7.7

fifth circle: πd = (3.14)(7.7) = 24.2

Move down to the circle with the diameter of 50

Sixth circle: πd = (3.14)(50) = 157.1

Move left to the circle with the radius of 11.8

Seventh circle: 2πr = 2(3.14)(11.8) = 74.1

Move down to the circle with the radius of 38

Eight circle: 2πr = 2(3.14)(38) = 238.8

Move right to the circle with the diameter of 1.1

ninth circle: πd = (3.14)(1.1) = 3.5

Move right to the circle with the radius of 14.8

10th circle = 2πr = 2(3.14)(14.8) = 93

Move up to the end.

Hope this helps :) 
7 0
3 years ago
How many times is 1 trillion greater than 1 billion
vodomira [7]

1 trillion can be written as 1,000,000,000,000

1 billion can be written as 1,000,000,000

There are 3 more 0’s in 1 trillion than there are in 1 billion, so therefore 1 trillion is 1,000 times greater than 1 billion.

If you have any further questions feel free to ask.

Hope this helps

8 0
2 years ago
Lijuan threw a softball 124 feet on her first throw. She threw the softball 30% farther on her second throw. On her third throw,
Ymorist [56]
Lijuan threw the ball 17.05 feet further on her third throw
5 0
3 years ago
Read 2 more answers
Please answer this with explanation. Please I really am struggling. I will mark you brainalist. Please solve it Please
Hatshy [7]

Answer:

13, 11, 4, 16, 6, 22

Step-by-step explanation:

<em>Let the second digit be x and the last digit be y</em>

Given:

  • Data set: 13, x, 4, 16, 6, y
  • Mean = 12
  • y = 2x or x = 2y

The mean of the data is the average. The average can be calculated by determining the sum of the terms and dividing it by the total digits.

\implies \text{Mean of data:} \ \dfrac{13 + x + 4 + 16 + 6 + y}{6} = 12

Let us substitute the value of y (2x) in the data.

\implies \dfrac{13 + x + 4 + 16 + 6 + 2x}{6} = 12

Now, add all the terms in the data and simplify.

\implies \dfrac{39 + x +2x}{6} = 12

\implies \dfrac{39 + 3x}{6} = 12

Distribute the denominators and simplify.

\implies \dfrac{39}{6} + \dfrac{3x}{6}  = 12

\implies  \dfrac{13}{2} + \dfrac{x}{2}  = 12

\implies  6.5 + \dfrac{x}{2}  = 12

Subtract 6.5 both sides and simplify.

\implies  6.5 + \dfrac{x}{2}  - 6.5 = 12 - 6.5

\implies \dfrac{x}{2} = 5.5

Use cross multiplication and simplify.

\implies x= 5.5 \times 2

\implies  x= 11

To determine the value of "y", simply substitute the value of "x" into the expression that represents the value of "y".

\implies y = 2x

\implies y = 2(11)

\implies y = 22

When the x and y values are substituted in the data, we get;

  • ⇒ 13, 11, 4, 16, 6, 22

Therefore, the data is 13, 11, 4, 16, 6, 22.

8 0
2 years ago
Other questions:
  • Which equation is the inverse of y = x2 + 16?<br> 0 y=x²-16<br> y=i -16<br> y=+-16<br> y = x2 - 4
    9·1 answer
  • Two eighths of a circle is what percentage
    6·2 answers
  • A local zoo has two large snakes. The anaconda is currently 5.23 meters long and grows 1.27 meters every month. The python is 4.
    8·1 answer
  • Engli
    13·1 answer
  • Yo can someone help me out (READ CAREFULLY)
    15·2 answers
  • Is it likely that the next 50 Sunday customers will spend an average of at least​ $40? Explain. Choose the correct answer below​
    8·1 answer
  • Help what is x<br> When x^5 is 225
    7·2 answers
  • Change x-2y=4 into slope-intercept form.
    7·1 answer
  • PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU B
    11·1 answer
  • Find the slope of a line that passes through the following points (3,2) (5,-3)
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!