Find the vertex and the axis of symmetry for the following functions.
a) y = 2x^3 + 4x
b ) y= -x^2+4x-5

Answers

Answer 1

Answer:

b

Step-by-step explanation:

its correct

Answer 2

Step-by-step explanation:

a)

y = 2x³ + 4x

a polynomial of 3rd degree cannot have an axis of symmetry.

it can only have a point of symmetry, like in this case.

(0, 0) is the point of symmetry, because due to the fact there is no squared term, any negative x values create exactly the same values (in absolute values) as their positive counterparts - just negative.

the vertex of a polynomial of 3rd degree is the point where the function changes directions.

that point for x³ is the origin, as it is for x. the factors only stretch the graph, but the vertex stays the same.

only if we had a term like (x+a)³ in the polynomial, this would shift the vertex.

so, the point of symmetry and the vertex are the same :

(0, 0).

b)

y = -x² + 4x - 5

the vertex form of a quadratic function is

f(x) = a(x − h)² + k

with (h, k) is the vertex.

x = h is the axis of symmetry.

we use "complete the square" to get it into that form.

-x² + 4x - 5 = -(x² - 4x + 5) = -(x - 2)² - 1

therefore,

y = -(x - 2)² - 1

h = 2, k = -1

the vertex is (2, -1)

the axis of symmetry is x = 2


Related Questions

what is the least common denominator in 6/x = 4/x-8 + 1

a) x-8
b) x^2-8
c) 8x
d) x(x-8)

Answers

Answer:

d) x(x-8)

Step-by-step explanation:

Both of the denominators in the problem have to be in the common denominator. It needs the x because of the 6/x and it also needs to have x-8 because of the right side of the equation.

Answer:

d x(x - 8).

Step-by-step explanation:

That would be x * (x - 8)

help i dont know the answer like seriously omg omg

Answers

The gcf is 6

so: 42+12= 6(7+2)

Answer:

see explanation

Step-by-step explanation:

the factors of 42 are 1, 2, 3, 6, 7, 14 ,  21, 42

the factors of 12 are 1, 2, 3, 4, 6, 12

common factors are 1, 2, 3, 6

GCF = 12

then

42 + 12 ← factor out 6 from each term

= 6(7 + 2)

What is the range for the set of data? 6, 7, 10, 12, 12, 13 11 7 6 13

Answers

Answer:

7

Step-by-step explanation:

the range is the difference between the highest and lowest value in a data set.

13 is the highest in the distribution

6 is the lowest in the distribution

13-6=7

Give brainliest, please!

Hope this helps :)

simplify
Please help ASAP ​

Answers

[tex]\dfrac{4v^2}{wu+u^2} \times \dfrac{7w+7u}{4v-8v^2}\\\\\\=\dfrac{4v^2(7w+7u)}{(wu+u^2)(4v-8v^2)}\\\\\\=\dfrac{4v^2 \cdot 7(w+u)}{u(w+u)\cdot 4v(1-2v)}\\\\\\=\dfrac{7v}{u(1-2v)}[/tex]

GIVE BRAINLY PLEASE HELP
Which figure correctly shows the line of symmetry

Answers

A line of symmetry is a line that cuts a shape into half

PLS HELP

A bag that holds 9 oranges, 4 plums, and 7 apples. A fruit is drawn at random. What is the probability that it is NOT a plum.

Answers

Answer:

80%

Step-by-step explanation:

9 + 4 + 7 = 20

1 out of 20 = 5%

4 plums = 20%

Answer:

4/5 or 80%

Step-by-step explanation:

So u add up all the fruits which is 20. And then then u make a fraction which is all fruits but not plums over all fruits. So it is 16/20. The 16 came from not having the plums bc there are 4 plums and 20 - 4 = 16. Simplified of 16/20 is 4/5 or %80.

2. A fish tank is shaped like a rectangular prism. 1 2 square feet. The area of the base of the fish tank is 6 The height of the fish tank is 3 feet. 2 What is the volume, in cubic feet, of the fish tank?​

Answers

Answer:

A. Makes the most sense. If you are using multiplication you'd get 18 1/16

Step-by-step explanation:

Select the correct answer from each drop-down menu. the expression above can also be written in the form . for this expression, a = , b = , and c = .

Answers

The value of a, b and c from the given expression above are 15, 1 and 4 respectively

Indices expression

Indices are written in form of exponential expression. Given the expression

[tex]\sqrt[4]{15}[/tex]

We are to write the expression in the form

[tex]a^{b/c}[/tex]

This is simplified as shown

[tex]\sqrt[4]{15}= 15^{1/4}[/tex]

Compare both expression

a = 15

b = 1

c = 4

Hence the value of a, b and c from the given expression above are 15, 1 and 4 respectively

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A ball is thrown upward from a height of 15 ft with an initial velocity of 5 ft/s. Use the equation h=-16t^2+5t+15 to answer the following questions. Round to the nearest tenth.

How long will it take for the ball to hit the ground (h=0)?


What is the height of the ball after 0.5 seconds?​

Answers

Answer:

1) 1.1 seconds

2) 13.5 feet

Part A

[tex]\rightarrow \sf -16t^2 + 5t + 15 = 0[/tex]

Apply quadratic formula:

[tex]\rightarrow \sf t= \dfrac{-5\pm \sqrt{5^2-4\left(-16\right)\cdot \:15}}{2\left(-16\right)}[/tex]

Simplify following

[tex]\rightarrow \sf t=-\dfrac{-5+\sqrt{985}}{32},\:t=\dfrac{5+\sqrt{985}}{32}[/tex]

In decimal form:

[tex]\rightarrow \sf t=-0.825 ,\:t=1.137[/tex]

Conclusion:

As time is be only positive: t = 1.1 seconds

Part B

[tex]\rightarrow \sf h=-16t^2 + 5t + 15[/tex]

insert t = 0.5

[tex]\rightarrow \sf h=-16(0.5)^2 + 5(0.5) + 15[/tex]

simplify

[tex]\rightarrow \sf h=13.5[/tex]

please help me with my math problem

Answers

Answer:

A

Step-by-step explanation:

sin 32=29.2/x

x=29.2/sin 32

Answer:

[tex]A.\:\:x =\frac{29.2}{\sin (32)\degree}[/tex]

Step-by-step explanation:

[tex]\huge \sin 32\degree =\frac{29.2}{x}[/tex]

[tex]\huge\implies x =\frac{29.2}{\sin (32)\degree}[/tex]

Evaluate 1/4 c + 3d when c = 6 and d = 7

Answers

Answer:

SolutioN :

Just plug in the values of c & d in the given expression and calculate :

[tex] \longrightarrow \bf \: \frac{1}{4} \times 6 + 3 \times 7[/tex]

[tex] \longrightarrow \boxed{\bf{ \frac{45}{2} }}[/tex]

Our final answer is 45/2 .

--------------HappY LearninG <3 -------

           [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]

       Evaluate 1/4c+3d when c=6, and d=7.

        [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]

       Replace c with 6, and d with 7:-

     [tex]\Large\text{$\displaystyle\frac{1}{4} (6)+3(7)$}[/tex]

[tex]\bigstar[/tex] On simplification,

   [tex]\Large\text{$\displaystyle\frac{1}{4} \times\frac{6}{1}+21$}[/tex]

[tex]\bigstar[/tex] On further simplification,

    [tex]\Large\text{$\displaystyle\frac{6}{4} +21$}[/tex]

[tex]\bigstar[/tex] On further simplification,

     [tex]\Large\text{$\displaystyle\frac{6}{4}+\frac{84}{4}$}[/tex]

[tex]\bigstar[/tex] Adding the numerators,

[tex]\Large\text{$\displaystyle\frac{90}{4}$}[/tex]

[tex]\bigstar[/tex] Finally, Reducing the fraction:-

[tex]\Large\text{$\displaystyle\frac{45}{2}$}[/tex]

[tex]\Uparrow[/tex] [tex]\mathbb{OUR\:SIMPLIFIED\:EXPRESSION}[/tex]

Good luck with your studies.

         [tex]\rule{50}{1}\smile\smile\smile\smile\smile\smile\rule{50}{1}[/tex]

IF a universal set U = {x:x belongs to N , x less or equal to 10} , A ={y:y = 2n , n belongs to N , n less than 5} and B ={z:z = 3n , n belongs to N , n less than 4}

Answers

Answer:

your answer is N = {xxx: =9n

A circle is centered at (−4, 9) and has a radius of 11.

What is the equation of the circle?

Answers

Answer:

  (x +4)² +(y -9)² = 121

Step-by-step explanation:

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

__

We are given that (h, k) = (-4, 9) and r = 11. When we put these values into the equation, it becomes ...

  (x -(-4))² +(y -9)² = 11²

We can simplify this a bit to ...

  (x +4)² +(y -9)² = 121

which transformation would take figure a to figure b

Answers

A reflection would take figure A onto Figure B
Answer: A reflection over the X-Axis

The radius of a circle is 8 centimeters. What is the circle's area?

Answers

Area of circle= pi x radius squared

R=8

8 x 8= 64

64 x pi= 201.06 squared cm
So the area of a circle can be found with the equation A=πr2

If the radius is 8 we plug 8 into the equation

A=π8^2

We then square 8 which is 64

We now have
A= π64

We multiply 64 and pie so

A=201.06

What is the range for the following set of measurements? 7.1 g, 9.8 g, 2.3 g, 8.5 g, 7.4 g, 5.7 g

Answers

Answer:

7.5

Step-by-step explanation:

you take the largest number (9.8) and subtract with the smallest number (2.3)

9.8-2.3= 7.5

What is the mean absolute deviation of 3 3 1 9 3 1 8

Answers

Answer:

2.57 or rounded to 1 sig digit just 3

Match the attributes to each three-dimensional shape that has the cross-section described.

Only consider cross-sections with whole number dimensions parallel to a side of one of the prisms or the base of the pyramid.

Quadrilateral A:
area of
16 square inches
Quadrilateral B:
perimeter of
24 inches
Quadrilateral C:
perimeter of
16 inches

Answers

The attributes to each three-dimensional shape that has the cross-section is 4,16 and 4.

What is a quadrilateral and parallelogram?

Any closed figure made by 4 line segments joined end to end in series is called a quadrilateral.

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

Given;

Quadrilateral A: area of 16 square inches

Quadrilateral B: perimeter of 24 inches

Quadrilateral C: perimeter of 16 inches

Now,

Quadrilateral A:

a^2=16

a=4

Quadrilateral B;

4a=24

a=6

Quadrilateral C:

4a=16

a=4

Therefore, the answers of quadrilaterals will be 4,6 and 4.

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Write a system of inequalities using the given graph

Answers

For dark line

(0,1)(-1,-4)

Slope

m=-4-1/-1=5

Equation in point slope form

y-1=5xy=5x+1

Put (0,0)

0<1

As line is dark sign is ≤

The inequality

y≤5x+1

For dashed line

(2,0)(0,-2)

Equation in intercept form

x/2-y/2=1x-y=2y=x-2

Put (0,0)

0>-2

Symbol is >

Inequality is

y>x-2

Find the value of X

Answers

Answer:

x = 14

Step-by-step explanation:

By tangent secant theorem

[tex] x^2 = 7(7+21)[/tex]

[tex]\implies x^2 = 7(28)[/tex]

[tex]\implies x ^2=196[/tex]

[tex]\implies x=\pm\sqrt{196}[/tex]

[tex]\implies x=\pm 14[/tex]

x can not be negative

[tex]\implies x=14[/tex]

A store owner puts in an order for product x and product y for a total of 4,000 units. it costs $0.10 per item to ship of product x and $0.04 per item to ship product y. if the total shipping cost is $352, which system of equations can be used to determine how much of product x and product y the store owner bought? startlayout enlarged left-brace 1st row x y = 4,000 2nd row 10 x 4 y = 352 endlayout startlayout enlarged left-brace 1st row 10 x 4 y = 4,000 2nd row x y = 352 endlayout startlayout enlarged left-brace 1st row x y = 4,000 2ndrow 0.1 x 0.04 y = 352 endlayout startlayout enlarged left-brace 1st row 0.1 x 0.04 y = 4,000 2nd row x y = 352 endlayout

Answers

The system of equations can be used to determine how much of product x and product y the store owner bought is x + y = 4,000

0.10x + 0.04y = 352

Simultaneous equation

product xProduct yTotal units of x and y = 4,000 unitsCost of shipping each product x = $0.10Cost of shipping each product y = $0.04Total cost of shipping = $352

The equation:

x + y = 4,000

0.10x + 0.04y = 352

Therefore, the system of equations can be used to determine how much of product x and product y the store owner bought is x + y = 4,000

0.10x + 0.04y = 352

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Answer:

C

Step-by-step explanation:

use technology to find the solution to the system: 8x - 4y = -24 4x - 12y = -32

Answers

The solution to the system of equation 8x -4y = -24, 4x - 12y = -32 is x = 19 / 8 and y = 5 / 4

How to find solution to the system of equation?

The solution of the system of equation can be found as follows:

8x -4y = -24

4x - 12y = -32

Multiply equation(ii) by 2

8x - 4y = -24

8x - 36y = -64

32y = 40

y = 40 / 32 = 5 / 4

8x - 4(5  / 4) = -24

8x - 5 = -24

8x = -24 + 5

8x = 19

x = 19 / 8

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I will multiply twenty negative numbers​ together, with fifteen positive numbers. If the value of my number is​ x, how does it compare to​ zero? Fill in the blank using​ >, <, ​ or, ​ = to make the statement true.
x enter your response here

Answers

Answer:

x = 27

Step-by-step explanation:

Finding variation constant :

k = y/xk = 18/9k = 2

Substituting in the equation y = kx, where y = 54 :

54 = 2xx = 54/2x = 27

What percent of 4c in each expression? *2a

Answers

The percentage of 4c that's the expression 0.04c will be is 1%.

How to calculate the percentage?

From the complete information, we are told to calculate the percentage of 0.04c from 4c.

This will be calculated thus:

= 0.04c/4c × 100

= 0.01

= 1%

Therefore, the percentage is 1%.

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a) plot the graph of y= 5 and 2x + y = 8
b) wirte down the coordinates of the point where they cross
explain the steps pls?

Answers

The graph is shown below. Then the linear system crosses each other at (1.5, 5).

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The linear equations are given below.

y = 5 ...1

2x + y = 8 ...2

The graph is shown below.

By equations 1 and 2. Then we have

2x + 5 = 8

     2x = 3

       x = 1.5

Then the lines cross each other at (1.5, 5).

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need help on this geometry problem

Answers

I think this is the answer see photo

Solve the system of equations below: 4x + 6y = 32 and 3x - 6y = 3
Pls show work will give brainliest :)

Answers

Answer:

x=5 y=2

Step-by-step explanation:

3x-6y=3

3x=3+6y

x=1+2y

Substitute x for 4x+6y=32

4+8y+6y=32

4+14y=32

14y=28

y=2

3x-12=3

3x=15

x=5

Select all the right triangles, given the length of the sides

Answers

Answer:

B, E

Step-by-step explanation:

Needs a 3:4:5 ratio, or, if it is an isosceles triangle, then n:n:nsqrt(3)

Which summation formula represents the series below?
1 + 2 + 6 + 24

Answers

Answer:

First one is the answer of the question u asked

Answer:

Option a: ∑⁵(n−1)! is the correct answer.

n=²

Step-by-step explanation:

Option a: ∑n=25(n−1)

By substituting the values of n and expanding the summation, we have,

(2−1)!+(3−1)!+(4−1)!+(5−1)!

Subtracting, we have,

1!+2!+3!+4!

Expanding the factorial,

1+(2∗1)+(3∗2∗1)+(4∗3∗2∗1)

Simplifying, we get,

1+2+6+24

Thus, the summation ∑⁵ (n−1)! represents the

n=2

series 1+2+6+24

Hence, Option a is the correct answer.


What is the value of the expression 30-(-6)?
0 -180
O -5
O 5
O 24

Answers

I believe it’s 24, sorry if i’m wrong.

Answer:

36? its not on there but that is it.

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