Find the axis of symmetry and the vertex of the graph of the function.
g(x) = 2x^2+12x+4

Answers

Answer 1

so hmmm from the equation we can see that is in "x terms" so the independent variable is "x", that tells us the parabola is a vertical one, leading term's coefficient is "2", that means it opens upwards like a bowl.

on a vertical parabola the axis of symmetry is the x-coordinate of its vertex, let's find the vertex of this one.

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{+4} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 12}{2(2)}~~~~ ,~~~~ 4-\cfrac{ (12)^2}{4(2)}\right)\implies \left( -3~~,~~4-\cfrac{144}{8} \right) \\\\\\ (-3~~,~~4-18)\implies (\stackrel{x}{-3}~~,~~-14)~\hfill \stackrel{\textit{axis of symmetry}}{x=-3}[/tex]


Related Questions

What is the value of

-8(17-12)
—————
-2(8-(-2)

-4
-2
2
4

Answers

Answer:

4

Step-by-step explanation:

smart

An airplane flies with a constant speed
of 820 miles per hour. How far can it
travel in 1 hour?

Answers

given:

820 miles

to find:

how far the airplane can travel in an hour.

solution:

x= v × t

x= 820 × 1

x= 820 miles

so, the airplane can travel 820 miles per hour.

How many lines of symmetry does the following figure have?

1

3

4

5​

Answers

Answer:

1

Step-by-step explanation:

It has 1 lines of symmetry

Hopes this helps

#ViolentJax

i need help with this question!!

Answers

it's not a solution to the system above

Jason customizes and sells water bottles. He must sell each water bottle for less than $15, otherwise then nobody may buy them. Which number line represents all the possible prices for which Jason could sell a water bottle and make a profit?

Answers

Answer:

i cant really tell because there is no real explannation

Step-by-step explanation:

Round 716.51 to the nearest hundredth
A. 716
B. 717
C. 716.51
D. 716.515






Thank you to everyone thats helping me!​

Answers

Answer:

c

Step-by-step explanation:

the number(1) with the place value hundreth has nothing after it so it stays the same

Answer:

I believe the answer would be 717. Correct me if I'm wrong but that is what I believe the answer is.

Step-by-step explanation:

Since the answer is talking about hundredth, you would look at the decimal.

The decimal states that its .51, which means it could not be 716, since the decimal is less than 50, so your answer SHOULD be B). 717

i do not know this answer

Answers

We know that 2+2 is 4.

34 - 4 is 30.

Therefore, the legnth, a, is half of thirty.

30/2 = 15

a = 15

Answer:

[tex]\bf a= 15\;\; millimetetrs[/tex]

Step-by-step explanation:

perimeter: 34 millimetetrs

perimeter= [tex]\tt a+2+a+2=34[/tex]

[tex]\tt 2a+4=34[/tex]

[tex]\tt 2a+4-4=34-4[/tex] (Subtract 4 from both sides)

[tex]\tt 2a=30[/tex] (Simplify)

[tex]\tt \cfrac{2a}{2}=\cfrac{30}{2}[/tex] (Divide both sides by 2)

[tex]\tt a=15[/tex]

Therefore, a= 15 millimetetrs.

~

i need help im stuck lol

Answers

Answer: Angle A = 120 degrees.

Step-by-step explanation:

Answer:

50 degrees sorry if wrong

Step-by-step explanation:

What happens when a base dissolves?

Answers

Answer:

When dissolved, bases release hydroxide ions, OH-(aq) into solution.

Step-by-step explanation:

Water is the product of an acid and base reacting. Chemists say that the acid and base cancel or neutralise each other, hence the reaction is known as "neutralisation"

Answer: It increases the concentration of OH- in solution.

Step-by-step explanation:

The radius of a circle is 5.9 centimeters. Enter the area of the circle, in square centimeters. Round your answer to the nearest hundredth.​

Answers

109.36 to nearest hundredth

A= pi x r x r

= pi x 5.9 x 5.9

= 109.3588....

Hope this helps!

Pierre has more money than alex.
if Pierre gave Alex £20 they would have the same amount.
if Alex gave Pierre £22, the Pierre would have twice as much as Alex.
How much does each one actually have?

Answers

Answer:

p = 2a-22

a= p-20

these will help you find the actual value

Step-by-step explanation:

this is not for the actual value

pierre = p

alex = a

p = a+20

p-20 = a

p+22 = 2a

p = 2a-22

PLS HELP Solve for x

Enter your answer in the box.​

Answers

Answer:

6

Step-by-step explanation:

If two secants are drawn from a point outside a circle, then product of one secant segment and its external part equal the product of the other secant segment and its external part.

(Secant-Secant Power Theorem)

(JG)(JH) = (JM)(JK)

(16) X (7) = (8+X)(8)

112=64+8X

8X=48

X=6

A triangular garden has it sides 45m,40m and 50m . Then, find the cost of fencing it's boundary at the rate of Rs.60 per meter.​

Answers

we should find perimeter.

45+40+50=135m.

then, we should multiply 135 and rate of per meter.

135×60=8100Rs.

Which graph shows the solution to 8y < 4x + 16? A. B. C. D.

Answers

Answer:

The answer is D.

Step-by-step explanation:

Find the boundary line, and then just shade the area.

y < 1/2x + 2

Answer:

d

Step-by-step explanation:

2023

pleaseeee helppp i’m running out of time

Answers

Answer:

Square Root of 162 ~ 12.727

Step-by-step explanation:

Simply do the Pythagorean Theorem!

a^2 + b^2 = c^2

This case we're solving for the long side which is the hypothenuse.

9^2+9^2= c^

81+81=c^

162=c^

Square root of 162

Which is 12.727

A new truck can travel 350 miles on 25 gallons of gas.
a
How far can it travel on 60 gallons of gas?
b.
What is the cars gas mileage (miles per gallon)?

Answers

Answer:

A. 840 miles

B. 14 miles per gallon

Step-by-step explanation:

A. 14 mi. per gal. x 60 = 840 miles

B. 350 mi./25 gal. = 14 miles per gallon

hope this helps :)

1. The truck can travel 840 miles on 60 gallons of gas.

2. The truck's gas mileage is 14 miles per gallon.

What is Proportion?

Proportion refers to the relationship or comparison between two quantities or parts of a whole. It is often expressed as a ratio or a fraction. In mathematics, a proportion states that two ratios or fractions are equal.

a)  We have, 25 gallons of gas corresponds to 350 miles.

Let's set up the proportion:

25/350 = 60/x

25x = 350 (60)

25x = 21,000

x = 21,000 / 25

x = 840

Therefore, the truck can travel 840 miles on 60 gallons of gas.

b) The truck can travel 350 miles on 25 gallons of gas.

Gas mileage = Distance / Gas consumed

Gas mileage = 350 miles / 25 gallons

Gas mileage = 14 miles per gallon

Therefore, the truck's gas mileage is 14 miles per gallon.

Learn more about Proportion here:

https://brainly.com/question/26974513

#SPJ2

Solve the following: A)4x-1/2=x+7
B)3x+2=2x+13/3
(Please help)

Answers

Answer:

A) x = 2.5

B) x = 7/3

Step-by-step explanation:

A) 4x - 1/2 = x + 7

4x - x = 7 + 1/2

3x = 7.5

x = 7.5/3

x = 2.5

B) 3x + 2 = 2x + 13/3

x +2 = 13/3

x = 13/3 - 6/3

x = 7/3

I hope this helps!

Name two sides that appear to be intersecting, but not perpendicular

Answers

Answer:

Two distinct lines intersecting each other at 90° or a right angle are called perpendicular lines. Here, AB is perpendicular to XY because AB and XY intersect each other at 90°. The two lines are parallel and do not intersect each other. They can never be perpendicular to each other.

Step-by-step explanation:

hope it helps, God bless!

Two distinct lines intersecting each
other at 90° or a right angle are called
perpendicular lines. Here, AB is
perpendicular to XY because AB and
XY intersect each other at 90° The
two lines are parallel and do not
intersect each other. They can never
be perpendicular to each other.

50 POINTS FOR QUESTION 24 thank u!!

Answers

Answer:

Each instalment = £27.45

Step-by-step explanation:

Given:

Price of work trolley = £59.90Deposit = £5

Remaining balance to be paid = Price of work trolley - deposit

                                                   = £59.90 - £5

                                                   = £54.90

If the remaining balance is to be paid in 2 instalments:

Cost of each instalment = remaining balance ÷ 2

                                        = £54.90 ÷ 2

                                        = £27.45

if the mean of 4 6 9 11 10 and k is 8 what is its median​

Answers

This is the answer:
9 is the median

dd2+2
edeeeeeeeeedvvvvvvvvvvvvvvvw[[kqpwgjwegkJ=J

Answers

Answer: umm what did you say?

Step-by-step explanation:

solve for X: x = −b ± √b²-4ac/2a

Answers

two correct answers :

x = -2c

or

x = -2b - 2c

4.289 rounded to the nearest tenth

Answers

4.3 is your answer :)

Please help me solve this question

Answers

Shannon mistakenly mixed up angles A and B. Notice the side 9 is opposite angle B and not angle A.

She should replace every copy of uppercase A with uppercase B. Also, she should replace lowercase 'a' with lowercase b

This is what her steps should look like

[tex]\frac{\sin B}{b} = \frac{\sin C}{c}\\\\\frac{\sin B}{9} = \frac{\sin 125^{\circ}}{12}\\\\B= \sin^{-1}\left(\frac{9*\sin 125^{\circ}}{12}\right) \approx 37.9^{\circ}\\\\[/tex]

Then we can find angle A like this

[tex]A+B+C = 180\\\\A = 180 - B - C\\\\A \approx 180 - 37.9 - 125\\\\A \approx 17.1^{\circ}\\\\[/tex]

Angle A is approximately 17.1 degrees.

Hello Brainilest Brains, I was wondering what 87x72 is. Please say the answer in the answer section below. Thanks for the help!

Answers

Answer:

6,264

Step-by-step explanation:

Answer:

6264

Step-by-step explanation:

72 x 8 = 576

576 x 10 = 5760

72 x 7 = 504

5760 + 504

6264

pls solve the following math from trigonometry ​

Answers

Step-by-step explanation:

[tex] \tan(2x) = 1.5[/tex]

Take the arc tangent,

[tex] \tan {}^{ - 1} ( \tan(2x) ) = \tan {}^{ - 1} (1.5) [/tex]

[tex]2x = 56.3[/tex]

[tex]x = 28.15[/tex]

b.

[tex](3 \cos(x) + 1)(2 \cos(x) + 3) = - 2[/tex]

[tex]6 \cos {}^{2} (x) + 11 \cos(x) + 3 = - 2[/tex]

[tex]6 \cos {}^{2} (x) + 11 \cos(x) + 5 = 0[/tex]

[tex]6 \cos {}^{2} (x) + 6 \cos(x) + 5 \cos(x) + 5 = 0[/tex]

[tex]6 \cos(x) ( \cos(x) + 1) + 5( \cos(x) + 1) = 0[/tex]

[tex](6 \cos(x) + 5)( \cos(x) + 1) = 0[/tex]

Set each factor equal to zero.

[tex]6 \cos(x) + 5 = 0[/tex]

[tex]6 \cos(x) = - 5[/tex]

[tex] \cos(x) = - \frac{5}{6} [/tex]

[tex]x = \cos {}^{ - 1} ( \frac{5}{6} ) [/tex]

[tex]x = 146.4[/tex]

For the second factor,

[tex] \cos(x) + 1 = 0[/tex]

[tex] \cos(x) = - 1[/tex]

[tex]x = 180[/tex]

So the answer for the second one is

146.4 and 180.

i need help i need help i need help i need help i need help i need help i need help i need help i need help i need help i need help i need help i need help i need help i need help i need help i need help

Answers

Answer: 176 cubic cm

Step-by-step explanation:

Formula for finding volume is l x w x h

The first rectangle on the bottom:

2 x 2 x 8 = 32

The second rectangle next to it:

3 x 6 x 8 = 144

Now add the two values to get the volume of the figure

144 + 32= 176

Find the volume of the triangular prism.
4 ft
8 ft
37 ht

Answers

Answer:

4 ft

Step-by-step explanation:

So to calculate the volume of a triangular prism, the formula is 4ft

Step-by-step explanation:

volume of prism = area of triangle * length

                            = 1/2*4*8*37

                            = 592ft^3

What is the greatest common factor of 6x^2+18x-36

Answers

Answer:

6

Step-by-step explanation:

the gretest common factor would be 6 because you can divide 6,18,and -36 by 6

A
group of friends were working on a student film that had a budget of $1300.
They spent all their budget on equipment and props. They used 55% of their
budget on props. How much money did they spend on equipment?

Answers

Subtract it using a calculator is the best way. 1300-55%=715
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