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
ZanzabumX [31]
3 years ago
6

PLEASE HELP WILL GIVE BRAINLY!!!!!!!!!What is the vertex of the graph of the function f(x) = x2 + 8x − 2 ?

Mathematics
2 answers:
vovangra [49]3 years ago
7 0
<h3>Answer: D.  (-4, -18)</h3>

===================================================

Explanation:

A graph is a nice addition (and it will likely help us see the vertex directly), but it isn't necessary because we can use the equation given to us. Though I recommend using a graphing calculator to confirm the answer.

The original function is the same as y = 1x^2+8x + (-2). We see that it is in the form y = ax^2+bx+c where

a = 1

b = 8

c = -2

Use the values of 'a' and b to get the value of h, which is the x coordinate of the vertex.

h = -b/(2a)

h = -8/(2*1)

h = -4

The x coordinate of the vertex is x = -4. Plug this into the original equation to get

f(x) = x^2+8x-2

f(-4) = (-4)^2 + 8(-4) - 2

f(-4) = -18

Plugging x = -4 into f(x) leads to y = -18. The point (-4, -18) is on the parabola. Furthermore, this is the vertex (h,k)

------------

Alternatively, you can complete the square as shown below

y = x^2 + 8x - 2

y = (x^2 + 8x) - 2

y = (x^2 + 8x + 0) - 2

y = (x^2 + 8x + 16 - 16) - 2

y = (x^2 + 8x + 16) - 16 - 2

y = (x+4)^2 - 18

y = 1(x+4)^2 - 18

y = 1(x-(-4))^2 - 18

The last equation is in the form y = a(x-h)^2 + k with (h,k) = (-4,-18) being the vertex. The 16 is the result of taking half of 8 and squaring that result. We have 16-16 = 0 to make sure that we don't change the equation and keep things balanced. This is the same as adding 16 to both sides. All of this is done so we can end up with the (x+4)^2 perfect square portion.You can expand out (x+4)^2 - 18 and you should get x^2+8x-2 again.

mafiozo [28]3 years ago
7 0
D is the answer

Because you need to rewrite in vertex form and use this form to find the vertex (h,k)

Which should get you to

(-4,-18)
You might be interested in
$6x + $15 ≤ $70<br><br><br> I have no idea- xd
Delvig [45]

Answer:

x = 9

Step-by-step explanation:

6 × 9 = 54

54 + 15 = 69, which is less than 70.

3 0
3 years ago
What is the value of x?<br> 21<br> 24<br> 32<br> 44
VMariaS [17]

Answer:

x = 21

Step-by-step explanation:

Because GJ is a diameter, the angle K is a right angle (90 degrees).

Thus, 4x + 6 = 90, and 4x = 84.  Thus, x = 21

7 0
3 years ago
Minimize Q=3x2+3y2​, where x+y=6.
weeeeeb [17]

Answer:

+(x + y) {}^{2}  = 6 {}^{2} \\ x {}^{2} + 2xy + y {?}^{2}  = 36

x {}^{2}  + y {}^{2}  = 36 - 2xy

q = 3(x {}^{2}  + y {}^{2} )

q = 3(36 - 2xy) = 108 - 6xy

5 0
2 years ago
The formula used to calculate simple interest is modeled by I=prt, where I=simple interest, p=principle, r=interest rate, and t=
asambeis [7]
<span>An alternative equivalent versions are:

</span><span>I = trp
</span><span>t= l/rp
</span><span>p= l/rt</span>
5 0
3 years ago
Read 2 more answers
a film canister in the shape of a cylinder has a height of 8 centimeters and a volume of the film canister. write an equation fo
uranmaximum [27]

Answer:

Part a) The equation for the volume of the film canister is

32\pi=\pi r^{2}(8)

Part b) The radius of the film canister is 2\ cm

Step-by-step explanation:

<u><em>The complete question is</em></u>

A film canister in the shape of a cylinder has a height of  8 centimeters and a volume of 32π cubic centimeters.

a. Write an equation for the volume of the film canister.

b. What is the radius of the film canister?

Part a) Write an equation for the volume of the film canister

we know that

The volume of a cylinder is equal to

V=\pi r^{2} h

where

r is the radius of the circular base

h is the height of the cylinder

we have

V=32\pi\ cm^3

h=8\ cm

substitute

32\pi=\pi r^{2}(8) ----> equation for the volume of the film canister

Part b) What is the radius of the film canister?

we have

32\pi=\pi r^{2}(8)

32\pi=8\pi r^{2}

Simplify

Divide by 8π both sides

4=r^{2}

square root both sides

r=2\ cm

8 0
3 years ago
Other questions:
  • Suppose that 3% of all athletes are using the endurance-enhancing hormone EPO (you should be able to simply compute the percenta
    9·1 answer
  • Drinks 1 pint of 2% 1 quart of 1 cup of 1 quart of
    8·1 answer
  • Find the value of x in the triangle shown below. Help me Geometry question please!!​
    10·1 answer
  • 20+x over 8+12/2=1 what does x equal
    14·1 answer
  • A triangular prism has base edges 3 cm, 5 cm, and 7 cm long. Its lateral area is 285 cm? What is the height of the prism?
    12·1 answer
  • Use the function f(x)=2^x/x to answer the question. Which combination could result in the function f(x)?
    6·1 answer
  • Step by step how to get 22.04 times 2.8 with work
    11·1 answer
  • . In a class of students the ratio of the number of students who like to play football and the number of students who like to pl
    15·1 answer
  • What's the difference between a linear expression and a linear equation?
    6·2 answers
  • Select the correct answer.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!