Determine the axis of symmetry and the vertex of the given function.

Answers

Answer 1

The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y=ax2+bx+c , the axis of symmetry is a vertical line x=−b2a .


Related Questions

i need help with this

Answers

Answer:

A) (-8, -16)

B) (0, 48)

C) (-4, 0), (-12, 0)

Step-by-step explanation:

A) the vertex is the minimum y value.

extremes of a function we get by using the first derivation and solving it for y' = 0.

y = x² + 16x + 48

y' = 2x + 16 = 0

2x = -16

x = -8

so, the vertex is at x=-8.

the y value is (-8)² + 16(-8) + 48 = 64 - 128 + 48 = -16

B) is totally simple. it is f(0) or x=0. so, y is 48.

C) is the solution of the equation for y = 0.

the solution for such a quadratic equation is

x = (-b ± sqrt(b² - 4ac)) / (2a)

in our case here

a=1

b=16

c=48

x = (-16 ± sqrt(16² - 4×48)) / 2 = (-16 ± sqrt(256-192)) / 2 =

= (-16 ± sqrt(64)) / 2 = (-16 ± 8) / 2 = (-8 ± 4)

x1 = -8 + 4 = -4

x2 = -8 - 4 = -12

so the x- intercepts are (-4, 0), (-12, 0)

I need help finding the answer

Answers

Answer c can you explain more

The sine of angle θ is 0.3.

What is cos(θ)? Explain how you know.

Answers

Answer:

cos(θ) = -0.95

Step-by-step explanation:

Remember the relation:

sin(θ)^2 + cos(θ)^2 = 1

So if we have:

sin(θ) = 0.3

we can replace that in the above equation to get:

0.3^2 + cos(θ)^2 = 1

now we can solve this for cos(θ)

cos(θ)^2 = 1 - 0.3^2 = 0.91

cos(θ) = ±√0.91

cos(θ) = ± 0.95

Now, yo can see that there are two solutions, which one is the correct one?

Well, you can see that the endpoint of the segment that defines θ is on the second quadrant.

cos(x) is negative if the endpoint of the segment that defines the angle is on the second or third quadrant.

Then we can conclude that in this case, the correct solution is the negative one.

cos(θ) = -0.95

Simplify. (x2+2x-4)+(2x-5x-3)​

Answers

Answer:

Step by Step Solution

More Icon

STEP

1

:

3

Simplify ——

x2

Equation at the end of step

1

:

3

((((2•(x2))-5x)-——)+2x)-3

x2

STEP

2

:

Equation at the end of step

2

:

3

(((2x2 - 5x) - ——) + 2x) - 3

x2

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using x2 as the denominator :

2x2 - 5x (2x2 - 5x) • x2

2x2 - 5x = ———————— = ———————————————

1 x2

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

2x2 - 5x = x • (2x - 5)

Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • (2x-5) • x2 - (3) 2x4 - 5x3 - 3

————————————————————— = —————————————

x2 x2

Equation at the end of step

4

:

(2x4 - 5x3 - 3)

(——————————————— + 2x) - 3

x2

STEP

5

:

Rewriting the whole as an Equivalent Fraction :

5.1 Adding a whole to a fraction

Rewrite the whole as a fraction using x2 as the denominator :

2x 2x • x2

2x = —— = ———————

1 x2

Polynomial Roots Calculator :

5.2 Find roots (zeroes) of : F(x) = 2x4 - 5x3 - 3

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

Hello, have anyone can help me to solve this question?

Answers

Answer:

24 days LCM

prime factor :

4- 2, 2

8-2,2,2

12- 2,2,3

largest factors- 2,2,2,3

2*2*2*3 = 24

Step-by-step explanation:

after allowing 20% discount an article is sold for rs.672 levying 12% VAT, find its market price​

Answers

The market price is Rs. 750 which was obtained by creating a mathematical relationship from the given parameters.

PERCENTAGE DISCOUNT = 20%

VAT LEVIED= 12%

PRICE SOLD = 672

Let the MARKET PRICE = m

Hence,

market price * (1 - discount) * (1 + VAT) = price sold

m * (1 - 20%) * (1 + 12%) = 672

m * (1 - 0.2) * (1 + 0.12) = 672

m * 0.8 * 1.12 = 672

0.896m = 672

m = 672 / 0.896

m = Rs. 750

Learn more :

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The Market Price of the product is RS. 750.

The Market Price is calculated by dividing the components associated to Discount, which is less than 1, and the Value Added Tax, which more than 1, to the Resulting Price.

[tex]c_{M} = \frac{c_{R}}{\left(1-\frac{r_{D}}{100} \right)\cdot \left(1+\frac{r_{T}}{100} \right)}[/tex] (1)

Where:

[tex]c_{M}[/tex] - Market price, in monetary units.

[tex]c_{R}[/tex] - Resulting price, in monetary units.

[tex]r_{D}[/tex] - Discount rate, in percentage.

[tex]r_{T}[/tex] - Tax rate, in percentage.

If we know that [tex]c_{R} = 672[/tex], [tex]r_{D} = 20[/tex] and [tex]r_{T} = 12[/tex], then the market price is:

[tex]c_{M} = \frac{672}{\left(1-\frac{20}{100} \right)\cdot \left(1+\frac{12}{100} \right)}[/tex]

[tex]c_{M} = 750[/tex]

The market price of the product is RS. 750.

State if the triangles are similar. If so, how do you know they are similar and complete the similarity statement.
ΔFED
~ ____

Answers

Answer:

FED ~ MLF

Step-by-step explanation:

∠L = ∠E

∠F = ∠F

Since both angles are congruent, that would mean all angles are congruent.

If all angles are congruent, then the triangles are always similar no matter the length of the sides.

The complete statement is [tex]\triangle FED\sim \triangle FLM[/tex].

What are the similar triangles?

Similar triangles are the triangles that have the same shape, but their sizes may vary.

What is AA or angle angle similarity rule?

If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

What are vertically opposite angles?

When two lines intersect each other, then the opposite angles are formed due to intersection are called vertical angles or vertically opposite angles.

According to the given question.

We have two triangles LMF and EDF

In triangles LMF and EFD we have

∠MLF = ∠DEF   (given)

Also, ∠MFL = ∠DFE   (vertically opposite angles)

Since, we know that " if any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other".

Therefore, by AA similarity criteria triangle FED is similar to FLM.

Hence, the complete statement is [tex]\triangle FED\sim \triangle FLM[/tex].

Find out more information about AA similarity rule and vertically opposite angles here:

https://brainly.com/question/10069556

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On a baseball field, the pitcher's mound is 60.5 feet from home plate. During practice, a batter hits a ball 226 feet at an angle
of 39° to the right of the pitcher's mound. An outfielder catches the ball and throws it to the pitcher. Approximately how far does
the outfielder throw the ball?

Answers

Answer:

183.0 ft

Step-by-step explanation:

The function f(t) = 4t2 − 8t + 7 shows the height from the ground f(t), in meters, of a roller coaster car at different times t. Write f(t) in the vertex form a(x − h)2 + k, where a, h, and k are integers, and interpret the vertex of f(t).

A) f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 3 meters from the ground
B) f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 1 meter from the ground
C) f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 2 meters from the ground
D) f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 1 meter from the ground

Answers

Answer:

A) f(t) = 4(t − 1)^2 + 3; the minimum height of the roller coaster is 3 meters from the ground

Step-by-step explanation:

f(t) = 4t^2 − 8t + 7

Factor out 4 from the first two terms

f(t) = 4(t^2 − 2t) + 7

Complete the square

(-2/2)^2 =1  But there is a 4 out front so we add 4 and then subtract 4 to balance

f(t) = 4( t^2 -2t+1) -4 +7

f(t) = 4( t-1)^2 +3

The vertex is (1,3)

This is the minimum since a>0

The minimun is y =3 and occurs at t =1

Answer:

The above answer is correct.

Step-by-step explanation:

Can anyone help me with this it’s question 2 help please

Answers

Answer: 2x³ + 2x² + 36

Working:

= (2x + 6) × (x² - 2x + 6)

= 2x³ - 4x² + 12x + 6x² - 12x + 36

= 2x³ -4x² + 6x² +12x -12x +36

= 2x³ + 2x² + 36

Answered by Gauthmath must click thanks and mark brainliest

I cannot see your question it’s blurry send me it

the sum of the fractions 2/y-3 and 6/y+3 is equal to their

Answers

Step-by-step explanation:

Move expression to the left side and change its sign

5

y

3

+

10

y

2

y

6

y

y

+

2

=

0

Write

y

as a sum or difference

5

y

3

+

10

y

2

+

2

y

3

y

6

y

y

+

2

=

0

Factor out

y

and

3

from the expression

5

y

3

+

10

y

(

y

+

2

)

3

(

y

+

2

)

y

y

+

2

=

0

Factor out

y

+

2

from the expression

5

y

3

+

10

(

y

+

2

)

(

y

3

)

y

y

+

2

=

0

Write all numerators above the least common denominator

5

(

y

+

2

)

+

10

y

(

y

3

)

(

y

+

2

)

(

y

3

)

=

0

Distribute

5

and

y

through the parenthesis

5

y

+

10

+

10

y

2

+

3

y

(

y

+

2

)

(

y

3

)

=

0

Collect the like terms

8

y

+

20

y

2

(

y

+

2

)

(

y

3

)

=

0

Use the commutative property to reorder the terms

y

2

+

8

y

+

20

(

y

+

2

)

(

y

3

)

=

0

Write

8

y

as a sum or difference

y

2

+

10

y

2

y

+

20

(

y

+

2

)

(

y

3

)

=

0

Factor out

y

and

2

from the expression

y

(

y

10

)

2

(

y

10

)

(

y

+

2

)

(

y

3

)

=

0

Factor out

(

y

10

)

from the expression

(

y

10

)

(

y

+

2

)

(

y

+

2

)

(

y

3

)

=

0

Reduce the fraction with

y

+

2

y

10

y

3

=

0

Determine the sign of the fraction

y

10

y

3

=

0

Simplify

10

y

y

3

=

0

When the quotient of expressions equals

0

, the numerator has to be

0

10

y

=

0

Move the constant,

10

, to the right side and change its sign

y

=

10

Change the signs on both sides of the equation

y

=

10

Check if the solution is in the defined range

y

=

10

,

y

3

,

y

2

y

=

10

Answer:

I think "Product" is the answer. Not really sure.

find the measure of the missing angles in the kite​

Answers

Answer: 360 - 44 - 80 = 236

236 ÷ 2 = 118

both angle equal to 118

Step-by-step explanation:

The measure of angle 1 is 118 degrees and the measure of angle 2 is 118 degrees.

What is quadrilateral?

It is defined as the four-sided polygon in geometry having four edges and four corners.

We know that kite is quadrilateral, having :

It has one pair of opposite congruent angles.

One diagonal is bisected.

The top and bottom angles are bisected but

As we know from the kite properties it has one pair of opposite congruent angles

From the properties of the quadrilateral the sum of the interior angles is 360 degrees

44 + angle 1 + angle 2 + 80 = 360

Angle 1 = angle 2 = x(say)

44 + x + x + 80 = 360

2x + 124 = 360

2x = 236

x = 118 degrees

Angle 1 = angle 2 = 118 degrees

Thus, the measure of angle 1 is 118 degrees and the measure of angle 2 is 118 degrees or m∠1 = 118° and m∠2 = 118°.

Learn more about the quadrilateral here:

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Calculate the average speed in km/h for a plane that travels 1300km in 4 hours??

Answers

Answer:

The plane is going 325 kilometers per hour :)

Step-by-step explanation:

To find the average speed per hour, divide 1300 by 4.

1300/4 = 325

Maritza is comparing cell phones plans and notices that verizon offers a plan that is $60 for 10GB of data and $12 for each extra GB of data ore month. Create an expression to model this situation

Answers

Answer:

60 + 12 * g, with g representing the number of extra gigabytes

Step-by-step explanation:

First, we know that Maritza has to pay $60 for 10GB of data, no matter what. Therefore, the base cost of the cell phone plan is 60 dollars, and all extra costs must be added to that. Currently, our expression is therefore 60 + something = cost of cell phone plan.

After that, the plan costs $12 for each gigabyte of data past 10 GB. This means that, for example, if Maritza uses 11 gigabytes, the plan will cost 60 (the base amount) + 12 for each gigabyte past 10 GB. There are 11-10=1 extra gigabytes, so the cost is 60 + 12 * 1 = 72 dollars. For each extra gigabyte, 12 dollars are added, so we can represent this as

60 + 12 * g, with g representing the number of extra gigabytes

On a map, two mountains are 5 7/8 inches apart. If 1/2 of an inch on the map represents 80 miles, then how many miles apart

Answers

Answer:

235 miles

Step-by-step explanation:

80(5 7/8÷ 2)

Help anyone can help me do this question,I will mark brainlest.​

Answers

Step-by-step explanation:

GIVEN =

d= 49cm

[tex]\pi = \frac{22}{7} [/tex]

To find = Circumference of a circle

SOLUTION =

CIRCUMFERENCE OF THE CIRCLE = πd

[tex] \frac{22}{7} \times 49[/tex]

= 22 × 7

154cm

the circumference of the given circle is 154cm

Answer:

Step-by-step explanation:

5) diameter = d = 49 cm

Circumference = πd

                         [tex]= \frac{22}{7}*49\\\\= 22 *7\\\\= 154 \ cm[/tex]

6) d = 20 mm

Circumference = π* 20

                         = 20π mm

determinar el decimal correspondiente
A)71% B)172% C)6%

Answers

[tex]71\% = \frac{70}{100} = \frac{7}{10} = 0.7 \\ 172\% = \frac{172}{100} = 1.72 \\ 6\% = \frac{6}{100} = 0.06[/tex]

BRAINLIEST graphing question

Answers

Answer:

Step-by-step explanation:

What type of number is 37 + 1?
Choose all answers that apply:
Whole number
Integer
Rational
Irrational

help

Answers

Answer:

Irrational

Step-by-step explanation:

The constant [tex]\pi[/tex], or "pi", is an irrational mathematic constant that corresponds to a non-terminating (never-ending decimal). Because there are an infinite number of digits in pi, pi cannot be expressed as a fraction and therefore is irrational.

Multiplying or adding a rational number does not make pi rational, and therefore the desired answer is (D) Irrational.

Find the value of each variable. Lines that appear tangent are tangent, and the dot is the center. (Answer in the form a=? b=? c=? d=?)

Answers

Answer:

a = 60°/2 = 30°

b = 84/2 = 42°

c = (100+60)/2 = 80°

d = 360-100-60-84 = 116°

Answered by GAUTHMATH

What would your position on the circle (cos q, sin q) be after rotating 72degrees from the point (1,0)?

A=(.97, .25)
B=(.31, .95)
C=(.95, .31)
D=(.25, .97)

Answers

Answer:

B=(.31, .95)

Step-by-step explanation:

When your at the point (1,0) you are at 0 degrees (cos 0, sen 0) = (1,0).

So at 72 degrees you moved 72 degrees (cos 72, sin 72) = (.31, .95)

evaluate : 8/-5+(4/-3)+1/3

Explain full steps
with easy method​

Answers

Answer:

-39/15

Step-by-step explanation:

=-8/5-4/3+1/3

Taking LCM of 5,3 and 3.

=3(-8)-5(4)+5(1)/15

=-24-20+5/15

=-44+5/15

=-39/15

Note:if you need to ask any question please let me know.

Using the intercept method, what are the two points to plot when graphing the line x + 3y = 6?

Answers

Answer:

The Slope-Intercept Form is essentially a special case of the Point-Slope Form. It's said that two points determine a line. That truism is used to quickly sketch a line if its equation is given in the Two Intercept-Form ax + by = c. We get the y-intercept by setting x = 0 and solving for y: by = c, y = c b .

Step-by-step explanation:

plzzz make brainlist and follow

Answer:

(0,2) and (6,0)

Step-by-step explanation:

y-intercept, x=0

0+3y=6

y=2

x-intercept, y=0

x=6

Help with step by step solution please

Answers

Answer:

5/2

Step-by-step explanation:

The square root of 5 divided by the negative square root of 5 equals -1. 7/2 - 1 = 5/2.

Given: PSTK is a rectangle
Area of PSTK=562m^2
m∠TOK=75
Find:PS, PK
(HELP! ILL GIVE BRAINLIEST)

Answers

Answer:

See picture below

Step-by-step explanation:

Let PK be the length and PS be the width of the rectangle.

Then LW =562

Assuming O is the center of the rectangle then ∠KST = ∠STO = 75/2

Hence tan ( 75/2 ) = PS/PK

Now solve the system of the equations

PS*PK=562

tan ( 75/2 ) = PS/ PK

8 to the power of 6 divided by 8 to the power of 2
PLZ HELP ASAP WILL MARK BRAINLIEST

Answers

Answer:

4096

Step-by-step explanation:

8^6÷8^2

First step is to solve the exponents

8 to the power of 6 is 262144

8 to the power of 2 is 64

Then divide 262144 by 64 : 4096

Answer:

it is a law of axponent that is a to the power m divided by a to the power n = a to the power m-n

so 8 to the power 6-2

= 8 to the power 4

that will be 4,096

Can you help with number 9,10,12

Answers

for question 9 the answer will be in the photo

Please help me factorise these brackets and expand them

Answers

Answer:

5ba^2 +ab^2 6a^2 + 2b

Step-by-step explanation:

ab(6a+b)-3a^2 (b-2)+2b(a^2 +1)

6ba^2 +ab^2 -3ba^2 +6a^2 + 2ba^2 +2b

6ba^2 -3ba^2 +2ba^2 +ab^2 +6a^2 +2b

5ba^2 +ab^2 6a^2 + 2b

pls answer quickly before 3:30

Answers

Lol good luck buddy lololololololol

Function g is the result of these transformations on the parent sine function:
-vertical stretch by a factor of 3
-horizontal shift left pi/2
-units vertical shift down 4 units
Below is the question from the Edmentum test :)

Answers

Answer:

g(x) = 3·sin(x + π/2) - 4

Step-by-step explanation:

The given (general form of a) sin function is g(x) = A·sin(x + C) + D

Where;

A = The amplitude (the vertical stretch) = 3

C = The phase shift, left = π/2

D = The vertical shift = 4 units down = -4

Therefore, given that in the parent function, we have f(x) = sin(x), by substituting the values of A, C, and D to complete the equation modeling the function g, we get;

g(x) = 3·sin(x + π/2) - 4

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