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
valkas [14]
2 years ago
5

Y=-x^2-12x-37 find the 1) Roots 2) Factors 3) Vertex (x,y) 4) Interception with 'Y" axis 5) Axis of Symmetry 6)Direction of Open

ing 7)Max / Min ? Coordinates 8)Sketch 9) Domain 10) Range
Mathematics
1 answer:
kakasveta [241]2 years ago
4 0

Answer:

1) The roots of the equation Y = -x² - 12·x - 37 are x = -6 - √73 and -6 + √73

2) The factors of the function Y = -x² - 12·x - 37 are (x + (-6 - √73)) and (x - (-6 + √73))

3) The vertex is (-6, -1)

4) The Y-intercept is (0, -37)

5) The axis of symmetry is x = -6

6) The parabola opens downward

7) The maximum point is (-6, -1)

8) The graph of the function created with Microsoft Excel is attached

9) The domain of the function is -∞ < x < ∞

10) The range of the function is -∞ < Y ≤ -1

Step-by-step explanation:

The given function is Y = -x² - 12·x - 37

1) The roots of the equation Y = -x² - 12·x - 37 is given as follows;

0 = -x² - 12·x - 37

∴ -x² - 12·x - 37 = 0

The roots are;

x = (12 ± √((-12)² - 4 × 1 × (-37)))/(-2)

∴ x = -6 - √73 and -6 + √73

2) The factors are (x + (-6 - √73)) and (x - (-6 + √73))

3) The vertex is given by h = -b/(2·a) = 12/(2) = -6

k = c - b²/(4·a) = -37 - 144/(-4) = -1

The vertex = (h, k) = (-6, -1)

4) The intercept with the "Y" axis is given when x = 0, therefore, the y-intercept is (0, -37)

5) The axis of symmetry can be found at the vertex or the line x = -6

6) The sign of the coefficient of x² is negative therefore, the parabola opens downward

7) The maximum point is given as follows;

At the maximum point, dY/dx = d(-x² - 12·x - 37)/dx = -2·x - 12 = 0

x = 12/(-2) = -6, which is the vertex, therefore Y = -(-6)² - 12×(-6) - 37 = -1

The maximum point is the vertex (-6, -1)

8) Please find attached the graph of the function created with Microsoft Excel

9) The domain of the function is -∞ < x < ∞

10) The range of the function is -∞ < Y ≤ -1

You might be interested in
A 13.5​-m fire truck ladder is leaning against a wall. Find the distance d the ladder goes up the wall​ (above the fire​ truck)
larisa86 [58]
To solve this problem you must apply the proccedure shown below:

 1. You have the the<span> 13.5​-m fire truck ladder is leaning against a wall and the ladder makes an angle of 39 degrees 45 ' with the horizontal.

 2. Then you have:

 3</span>9 degrees 45'=39.75°
<span>
 Sin(39.75°)=d/13.5
 d=13.5x</span>Sin(39.75°)
<span> d=8.63

 </span>
8 0
3 years ago
Read 2 more answers
Micheal is 5 years older than Rui Feng and Vishal is thrice as old as Micheal if Rui Feng is p years old, find i) Michael's pres
Kitty [74]

Answer:

Michael's present age = p + 5

Michael's present age = 3p + 15

Sum of there ages 6 year age = 5p + 38

Sum of there ages 3 year ago = 5p - 11

Step-by-step explanation:

Assume;

Age of Rui Feng = x

Age of Micheal = x + 5

Age if Vishal = 3[x+5]

Given:

Age of Rui Feng = P

Computation:

Michael's present age = Age of Rui Feng + 5

Michael's present age = p + 5

Vishal's present age = 3[p + 5]

Michael's present age = 3p + 15

Sum of there ages 6 year age = [p + 6] + [p + 5 + 6] + 3[p + 5] + 6

Sum of there ages 6 year age = 5p + 38

Sum of there ages 3 year ago = [p - 3] + [p + 5 - 3] + 3[p + 5] - 3

Sum of there ages 3 year ago = 5p - 11

8 0
2 years ago
A circle is centered at the point (5,-4) and passes through (-3,2). The equation of this circle is (x+___)²+(y+___)²=____.
JulsSmile [24]
The equation of a circle is:
 (x-h)^2 + (y-k)^2 = r^2
 where (h,k) is the location of the center and r is the radius.  So we need to find h, k, and r.  The center is given as (5,-4) so h = 5 and k = -4:
 (x-5)^2 + (y-(-4))^2 = r^2
 (x-5)^2 + (y+4)^2 = r^2
 So we need to find r.  Use the distance formula to find the distance between (5,-4) and (-3,2):
 r = [(5-(-3))^2+((-4)-2)^2]^1/2
 r = [8^2 + (-6)^2]^1/2
 r = [64 + 36]^1/2
 r = 100^1/2
 r= 10
 The final equation is:
 (x-5)^2 + (y+4)^2 = 10^2
7 0
3 years ago
0.0345 Mm to meters?
olga_2 [115]
0.0344 millimeters= 3.45 meters
5 0
2 years ago
Read 2 more answers
Audrey is making a dress from a pattern. She has recently been learning about the area of a rectangle. She has two rectangular p
Nitella [24]

Answer:

51500

Step-by-step explanation:

Area (of the first piece) = l*w

125 * 412 = 51500

3 0
3 years ago
Read 2 more answers
Other questions:
  • 2 to the power of 2 + 1<br> 5
    6·2 answers
  • If y varies directly as x, and y =15 as x= -3, find y for the x-value of 6.
    8·1 answer
  • One side of a rectangular football field's width is equal to 55 yards. One side of the field's length is 110 yards. Calculate th
    12·1 answer
  • Evaluate 5 - 3(-2) + 1-3|​
    10·2 answers
  • What is the answer to 6÷2(1+2)
    5·2 answers
  • What is the solution to the following system of equations?
    7·1 answer
  • Snow is 0.02 m deep after 1 hour and 0.06 m deep after 3 hours. State the independent variable and the dependent variable. Then
    11·1 answer
  • What is one twelve of 1
    5·1 answer
  • What is the degree of one and a half full turns
    11·1 answer
  • 3) Which inequality represents this scenario?
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!