Identify the key features of these functions:

f(x) = 3(x + 5)2 − 10

g(x) = 200(0.95)x

h(x) = -0.25(x + 3)(x − 1)

The vertex of f(x) is at
. The function g(x) is decreasing at a rate of
%. The zeros of h(x) are at
and
.

Answers

Answer 1

Answer:

The vertex of f(x) is at (-5,-10).

The function g(x) is decreasing at a rate of 5%.

The zeros of h(x) are at x = -3 and x = 1.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, f(x_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]f(x_{v})[/tex]

Decaying exponential function:

A decaying exponential function has the following format:

[tex]A(x) = A(0)(1-r)^{x}[/tex]

In which A(0) is the initial quantity and r is the decay rate.

Zeros of a function:

Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.

Vertex of f:

The function f is given by:

[tex]3(x+5)^2 - 10[/tex]

Expanding the calculations to place at the correct format:

[tex]3(x+5)^2 - 10 = 3(x^2 + 10x + 25) - 10 = 3x^2 + 30x + 75 - 10 = 3x^2 + 30x + 65[/tex]

Which means that

[tex]a = 3, b = 30, c = 65[/tex]

The x-value of the vertex is:

[tex]x_{v} = -\frac{30}{2*3} = -5[/tex]

The y-value of the vertex is:

[tex]f(-5) = 3(-5+5)^2 - 10 = -10[/tex]

The vertex of f(x) is at (-5,-10).

Decreasing rate of g(x).

We have that:

1 - r = 0.95

So

r = 1 - 0.95 = 0.05

Which means that the decreasing rate is of 5%.

The zeros of h(x) are

The zeros are

x + 3 = 0 -> x = -3

x - 1 = 0 -> x = 1

So

The zeros of h(x) are at x = -3 and x = 1.


Related Questions

Round 7.954 to the place named.
Hundredths

Answers

Answer:

The answer is 7.95

Step-by-step explanation:

I hope I helped.

-2 (1/3x - 1/5) please answer ASAP I have to turn this in in 30 min!!

Answers

Answer:

1/3 + 1/5 them you solve -2

Step-by-step explanation:

Answer:

-2/3x+2/5

Step-by-step explanation:

Open up parentheses

-2 x 1/3x= -2/3x

-2 x 1/5= 2/5

Solve the system of linear equations by graphing.
y = x-7
y = -2x + 5

Answers

Answer:

4

Step-by-step explanation:

Find values for a and b so that 2(3x+5)+ax=5(4x−b) is an identity equation.

Answers

Answer:

a=30 b=2 (not sure)

Step-by-step explanation:

Simplify first part : 2*3x+ 2*5= 6x+10+ax

Simplify 2nd part : 5*4x-5*b. 5x-5b

we have: 6x+10+ax=20x-5b.

we minus 6x from both sides

10+ax=14x+5b

Minus 10

ax=14x+5b-10

Divide x

a=14+5b-10

a=4+5b

divde 5

a/5= 4+b

perhaps it is 30

30/5=4+b

6=6

but i am not sure

please help i will give brainliest

Answers

Answer:

437/4x^5/328^1/2-445^1/21

Step-by-step explanation:

hope this helps...

have a nice day

Find the midpoint M of the line segment joining the points P=(4,-7) and Q=(-6,-3)

Answers

Answer:

midpoints (-1, -5)

Step-by-step explanation:

midpoints

[tex] ( \frac{4 + ( - 6)}{2} \: \frac{ - 7 + ( - 3)}{2} )[/tex]

[tex]( \frac{4 - 6}{2} \: \frac{ - 7 - 3}{2} )[/tex]

[tex]( \frac{ - 2}{2} \: \frac{ - 10}{2} )[/tex]

[tex]( - 1 \: - 5)[/tex]

6/5 of ______ is 30
Please help

Answers

6x30=180
—————-
5x1= 5
180/5=36
5/5 =1
36/1
Answer : 36

It is 36.

180/5 = 36

5/5 = 1

When we put that together, we can see that our complete answer is:

36/1  

The complete and simplified answer to the question what is 6/5 of 30 is:

36.

PLEASE HELP. I WILL GIVE BRAINLIEST TO THE PERSON WHO ANSWERS BOTH PARTS OF THE QUESTION.



Parking at the posh center costs d dollars per hour during the off hours and an extra $3 per hour during peak hours. During holidays, the basic rate of d doubles. Write an expression for how much it would cost to park for 3d hours on a holiday during peak hours.
Then, if the basic off-hours parking rate is $2.50 per hour, how much would a person pay to park for 3d hours in the situation described above?


PLEASE HELP. I WILL GIVE BRAINLIEST TO THE PERSON WHO ANSWERS BOTH PARTS OF THE QUESTION.

Answers

THINGS TO REMEMBER:

the variable d represents dollarsCosts an extra $3 per hour during peak hoursWhile holiday's are going on the amount of d doublesFind how much parking would cost on a holiday during peak hour's

-----

Question: Write an expression for how much it would cost to park for 3d hours on a holiday during peak hours.

-----

Answer: 3d × 2  or  3d + 3d

-----

Explanation: This is because during holidays the amount of d doubles. However since this is on a holiday DURING peak hours it would be 3d × 2

-----

Question 2: Then, if the basic off-hours parking rate is $2.50 per hour, how much would a person pay to park for 3d hours in the situation described above?

-----

Answer: $15

-----

Explanation: Since d represents dollars we would multiply 2.50 times 3 which would give us 7.5 then we double this since it is during holidays giving us $15

-----

NOTE: I AM SO SORRY IF THIS IS WRONG AND I MISSED SOMETHING. IF IT IS WRONG THEN PLEASE MAKE SURE TO TELL ME SO I CAN FIGURE OUT WHAT I MISUNDERSTOOD

Again I'm sorry but I hope I helped a little bit.    

A house was valued at $292,000 . Over several years, the value increased by 8%, giving the house a new value.

Answers

Answer:

315,360 I had to assume you needed that number, 292000+8%=315360

if you were to roll two standard six-sided dice, what is the probability that both land on a 3 or greater

Answers

Answer:

4/9

Step-by-step explanation:

P(≥3 and ≥3) = 4/6 x 4/6 = 4/9

A LOT OF POINTS!!!! PLZ ANSWER

Answers

Answer:

f(3x)= 3x+5/6x+2

substitute the value of X in the given question.

if u want simplified form then u can try rationalising.

f(3x)= 3x+5/6x+2 hope helped thanks for points

Kelly is reading a 440-page book. During the past 5 days she has read 275 pages. At this rate, how many more days will it take her to complete the book? 3 days Ada​

Answers

3 days, 275/5=55 pages/day. 440-275=165. 165/5=3

What is the volume of the triangular prism below?
7 yd
18 yd
12 yd

Answers

Step-by-step explanation:

V = 1/2 a x c x h

1/2 * 7*12*18 = 756 yd ^3

Which number is an integer?

Answers

Answer:

there is no question for me to tell you what it is

1. What is the value of n in -57 - n = -144?
A-201
B-87
C 87
D 201

Answers

It’s 24.20 I took this quiz

Answer:

C=87

Step-by-step explanation:

To isolate the variable, you need to take away -57 by adding it to -144.

Then, you'd see:

-n=-87

Next, you divide both sides by -1 to get 87

The prom committee has no more than $600 to spend on centerpieces for the prom. If each centerpiece costs $25, what is the maximum number of centerpieces the committee can buy?

Answers

Answer:

600/25 = 24

Brainiest plz :)

Answer:

600/25 = 24

Have a good day I hope this helps.

i will give brainiest! i have to turn this in tonight please hurry.

Answers

9514 1404 393

Answer:

  (c)  24 minutes

Step-by-step explanation:

The rate of working problems differs by ...

  (1 problem)/(1.5 minutes) - (1 problem)/(2 minutes)

  = (2/3 -1/2) problems/minute

  = 1/6 problems per minute

So, to make up the difference of 4 problems will take ...

  time = quantity/rate = (4 problems)/(1/6 problem/minute) = 24 minutes

Caroline and Chase will be on the same problem after 24 minutes.

_____

Additional comment

Technically speaking, Chase will just be finishing problem 26 when Caroline starts it after 19.5 minutes. At that point in time, they are on the same problem. The answer choices suggest the real question is, "after how many minutes will they be starting the same problem at the same time?" After 24 minutes, both will be starting problem 29 at the same time.

Evaluate 6 * 2 ^ x for a) x = - 2 and (b) x = 3 . Write your answers in simplest form.

Answers

Answer:

a. [tex]\frac{3}{2}[/tex] b. 48

Step-by-step explanation:

(a) The value of the expression when x = -2 is 1.5.

(b) The value of the expression when x = 3 is 48.

What is a function?

A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output. There is a range, co-domain, and domain for every function.

Given that the expression is 6(2)ˣ.

To evaluate the expression 6(2)ˣ for different values of x, we simply substitute the value of x into the expression and simplify.

(a) When x = -2, we have:

6(2)⁻² = 6(1/4) = 1.5

So the value of the expression when x = -2 is 1.5.

(b) When x = 3, we have:

6(2)³ = 6(8) = 48

So the value of the expression when x = 3 is 48.

To learn more about the function;

brainly.com/question/28303908

#SPJ2

You roll a 6-sided die.
What is P(even)?
Write your answer as a percentage.

Answers

3/6 50% ? I believe so if I’m wrong sorry but I’m pretty sure it’s 50% hope this helped

On a map, 2.7 inches = 60 miles. How far apart are two cities if they measure 4.5 inches
apart on the map?

Answers

Answer:

120 miles

Step-by-step explanation:

2.7 times 2 is 4.5, so 60 times 2 is 120 (you're basically doubling both.)

You can purchase 2 sodas for 3 dollars, how much does 6 sodas cost?

Answers

Answer:

It costs $9

Step-by-step explanation:

Lets look at the ratio:

2/3

We need x:

6/x

Make an equation using the butterfly method:

3(6) = 2x

Simplify:

18=2x

Divide both sides by 2:

x=9

It costs $9

if you purchase 2 sodas it’s $3, 4 sodas it’s $6, and 6 sodas it’s $9. so it would be $9

which of the following is the slope of the line that passes through the points (-2,8) and (10,-1)

Answers

Slope of the line = increase in y/ increase in x
8 - - 1 / -2 - 10
9 / -12
= 3/-4
Slope of the line = 3/-4

Dora is thinking of a number between 500 and 600
When she divides it by a 1-digit number it has a remainder of 4
What could Dora’s number be?

Answers

9514 1404 393

Answer:

  500 ÷ 8 = 62 r 4, for example

Step-by-step explanation:

In order to have a remainder of 4, the divisor must be greater than 4, so could be any of 5, 6, 7, 8, 9.

The corresponding numbers could be any of ...

  504 +5n . . . 0 ≤ n ≤ 19

  502 +6n . . . 0 ≤ n ≤ 16

  501 +7n . . . 0 ≤ n ≤ 14

  500 +8n . . . 0 ≤ n ≤ 12

  508 +9n . . . 0 ≤ n ≤ 10

__

For example, with the divisor being 6, and n=13, the number could be ...

  580 = 6·96 + 4

1. Select all equations that are equivalent to (5x+6) over 2 =3-(4x + 12). A5+6= 3 - (4x + 12) (5x+6) B. 2 = -4x -9 c. x+3 = 3 – (4x + 12) (5x+6) = -4x + 15 2 E. 5x + 6 = -8x – 18​

Answers

Answer:

Only option E is equivalent to [tex]5x+6=-8x-18[/tex].

Step-by-step explanation:

Given the expression

(5x+6) over 2 = 3-(4x + 12)

Let us simplify the expression

[tex]\frac{\left(5x+6\right)}{2}=3-\left(4x+12\right)[/tex]

Multiply both sides by 2

[tex]\frac{5x+6}{2}\cdot \:2=3\cdot \:2-\left(4x+12\right)\cdot \:2[/tex]

[tex]5x+6=6-\left(4x+12\right)\cdot \:2[/tex]

Expand -(4x + 12) = -4x - 12

[tex]5x+6=-8x-18[/tex]

Thus, option E is equivalent to [tex]5x+6=-8x-18[/tex].

Further solving

[tex]5x+6=-8x-18[/tex]

Add 8x from to both sides

[tex]5x+8x=-8x-24+8x[/tex]

Simplify

[tex]13x=-24[/tex]

Divide both sides

[tex]\frac{13x}{13}=\frac{-24}{13}[/tex]

Simplify

[tex]x=-\frac{24}{13}[/tex]

Thus, only option E is equivalent to [tex]5x+6=-8x-18[/tex].

Answer:

E. 5x + 6 = -8x – 18​

Step-by-step explanation:

Hope this will help

help me out yall pleaseeee

Answers

opens downward. x-intercept=(-10,0),(6,0). axis of symmetry=x=-2. maximum=(-2,128)

Kevin made 4 of his 6 shots on goal at soccer practice if he continues to shoot in the same manner throughout the practice how many shot would he make out of 72

Answers

he would make 36 shots i think

The length of a rectangular painting is 3 inches longer than its width. If the diagonal is 15 inches long, what is the length of the painting?
A 9 inches
В. 12 inches
C. 13 inches
D. 18 inches

Answers

Answer:

Step-by-step explanation:

HELP PLEASE !!
Ivanna is riding on a bike course that is 15 miles long. So far, she has ridden 6 miles of the course. What percentage of the course has Ivanna ridden so far?

Answers

Answer:

50%

Step-by-step explanation:

24 divided by 2 times 5 then square foot of it

Answers

Answer:

7.75

Step-by-step explanation:

sq rt of (24/2)(5) = sq rt of 60 = 7.75

Answer:

7.75 rounded

Step-by-step explanation:

24 / 2 = 12

12 * 5 = 60

7.7459

rounded its 7.75

Richard bought 3 peaches and 1 orange and spent $3.50. Peaches are $0.85 each. If there is no sales tax on fruit, how much did the orange cost?

A.$0.66

B.$0.88

C.$0.95

D.$2.65

Answers

C You want to take $0.85 and multiply it by 3 for the 3 peaches and you get $2.55 then you do $3.50-2.55= $0.95

Answer:

D. $2.65

Step-by-step explanation:

0.85 x 3 = 2.55

The orange cost 10 cents.

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