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
slavikrds [6]
3 years ago
7

Describe the key features of the graph of the quadratic function f(x) = x2 - 8x - 20

Mathematics
1 answer:
Zolol [24]3 years ago
7 0
If f(x)=x^2-8x-20 then

dy/dx=2x-8 and d2y/dx2=2

A) Since acceleration is a constant positive the parabola opens upward.

B) Since acceleration is a constant positive the parabola will have a vertex at an absolute minimum

C)  The vertex will occur when dy/dx=0, 2x-8=0, 2x=8, x=4

So the axis of symmetry is the vertical line x=4.

The vertex is y(4)=-36, corresponding to the vertex point (4,-36)

The y-intercept occurs when x=0, y(0)=-20, so the y-intercept is the point (0,-20)
You might be interested in
Solve the equation. StartFraction dy Over dx EndFraction equals5 x Superscript 4 Baseline (1 plus y squared )Superscript three h
dangina [55]

Answer:

Step-by-step explanation:

To solve the differential equation

dy/dx = 5x^4(1 + y²)^(3/2)

First, separate the variables

dy/(1 + y²)^(3/2) = 5x^4 dx

Now, integrate both sides

To integrate dy/(1 + y²)^(3/2), use the substitution y = tan(u)

dy = (1/cos²u)du

So,

dy/(1 + y²)^(3/2) = [(1/cos²u)/(1 + tan²u)^(3/2)]du

= (1/cos²u)/(1 + (sin²u/cos²u))^(3/2)

Because cos²u + sin²u = 1 (Trigonometric identity),

The equation becomes

[1/(1/cos²u)^(3/2) × 1/cos²u] du

= cos³u/cos²u

= cosu

Integral of cosu = sinu

But y = tanu

Therefore u = arctany

We then have

cos(arctany) = y/√(1 + y²)

Now, the integral of the equation

dy/(1 + y²)^(3/2) = 5x^4 dx

Is

y/√(1 + y²) = x^5 + C

So

y - (x^5 + C)√(1 + y²) = 0

is the required implicit solution

5 0
3 years ago
6. When you barter, you must ________ <br> in order to buy something.
Lubov Fominskaja [6]

Answer:

When you barter, you must trade it for something else in order to buy something.

Step-by-step explanation:

8 0
3 years ago
What is the equation for the line of reflection <br>a. x= 3 <br>b. y = 3 <br>c. y = x <br>d. x = 6​
Stells [14]

Answer:

The answer to that question is c. y = x

8 0
3 years ago
Jordan is cutting a 2 meter by 1 1/4 meter into two pieces by its diagonal line
Airida [17]

Question:

Jordan is cutting a 2 meter by 1\frac{1}{4} meter piece of rectangular paper into two pieces along its diagonal. what is the area of each of the pieces?

Answer:

Area of each piece of paper is 1 \frac{1}{4} \ m^2.

Solution:

Length of the paper = 2 m

Width of the paper =  1\frac{1}{4} m =  \frac{5}{4} m

<em>Area of the rectangle = length × width</em>

                                    $=2\times \frac{5}{4}

                                    $= \frac{5}{2} \ m^2

<em>Diagonal of a rectangle divides it into two equal parts.</em>

Area of each piece = Area of the rectangle ÷ 2

                                $=\frac{ \frac{5}{2}}{2}

                                $=\frac{5}{4} \ m^2

                                $=1 \frac{1}{4} \ m^2

Area of each piece of paper is 1 \frac{1}{4} \ m^2.

7 0
3 years ago
A number is divided in the ratio 7:4.If the first part is 105,find the number
Gre4nikov [31]
105/7 = 15
15x4= 60

105:60

I think
3 0
3 years ago
Other questions:
  • Angle JKL is 54 degrees. What is the measure of angle MKL? *
    6·1 answer
  • With interest of $1,832.00 and a principal of $16,000 for 206 days, using the ordinary interest method, the rate is:
    7·1 answer
  • Which of the following is a solution of y |x|-6. (-5,1) (-1,-5) (5,-1)
    6·2 answers
  • Which is a solution to the system of inequalities? y≤-1/2x+3 y≥x+1
    15·1 answer
  • A number line contains points Q, R, S, and T. Point Q is on the coordinate 4, R is on the coordinate 8, S is on the coordinate 9
    13·1 answer
  • tmara is making a medium length necklace. write an expression that shows how nuch it will cost tamara for the chain,pendant,and
    9·1 answer
  • A garden supply store sells two types of lawn mowers. The smaller mower costs $249.99 and the larger mower costs $329.99. If the
    9·1 answer
  • Please help me out!!!!!
    7·1 answer
  • What is the answer to this geometry problem.
    14·1 answer
  • Solve the following equation for <br><br><br> G:2 (g-h) = b+4
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!