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
coldgirl [10]
3 years ago
10

What is the vertex of f(x)=-x^2-8x

Mathematics
2 answers:
frez [133]3 years ago
7 0

\bf f(x) = -x^2-8x\implies f(x) = -x^2-8x+0 \\\\[-0.35em] ~\dotfill\\\\ \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{-8}x\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{-8}{2(-1)}~~,~~0-\cfrac{(-8)^2}{4(-1)} \right)\implies \left( -4~~,~~0+\cfrac{64}{4} \right)\implies (-4~,~16)

Tatiana [17]3 years ago
7 0

Answer:

<h2>(-4, 16)</h2>

Step-by-step explanation:

\text{The vertex form of a parabola}\ f(x)=ax^2+bx+c:\\\\y=a(x-h)^2+k\\\\(h,\ k)\ -\ \text{vertex}\\\\\bold{METHOD\ 1}\\\\\text{complete to the perfect square}\ (a+b)^2=a^2+2ab+b^2\qquad (*)\\\\f(x)=-x^2-8x=-x^2-2(x)(4)=-x^2-2(x)(4)-4^2+4^2\\\\=-(\underbrace{x^2+2(x)(4)+4^2}_{(*)})+4^2=-(x+4)^2+16=-(x-(-4))^2+16\\\\h=-4,\ k=16\to\text{vetrex}=(-4,\ 16)

\bold{METHOD\ 2}\\\\\text{use the formula:}\\\\h=\dfrac{-b}{2a},\ k=f(h)\\\\f(x)=-x^2-8x\to a=-1,\ b=-8,\ c=0\\\\\text{substitute:}\\\\h=\dfrac{-(-8)}{2(-1)}=\dfrac{8}{-2}=-4\\\\k=f(-4)=-(-4)^2-8(-4)=-16+32=16\\\\\text{vertex}=(-4,\ 16)

\bold{METHOD\ 3}\\\\\text{Find the zeros of}\ f(x):\\\\f(x)=-x^2-8x\\\\f(x)=0\to-x^2-8x=0\\\\-x(x+8)=0\iff -x=0\ \vee\ x+8=0\\\\x=0\ \vee\ x=-8\\\\h\ \text{is halfway between zeros}.\\\\h=\dfrac{0+(-8)}{2}=\dfrac{-8}{2}=-4\\\\k=f(h)\to k=f(-4)=-(-4)^2-8(-4)=-16+32=16\\\\\text{vertex}=(-4,\ 16)

You might be interested in
N–2=10n+4/2 what is the value of n need help asap
MakcuM [25]
N - 2 = 10n + 4/2

-2 = 9n + 4/2

-4/4 = 9n

-1 = 9n

-9 = n

N is -9.

If this answer is right please leave a thanks and a rating. :)
4 0
2 years ago
4 men can finish a job in 7 days how many more people are needed to finish the job in 4 days?
Luden [163]

Answer:

this makes no sense but i already answered so ima say 1

Step-by-step explanation:

im so sorry

7 0
2 years ago
I’m confused and need help fast please.
Vikki [24]

Answer:

C) 48.3

Step-by-step explanation:

The lines are parallel, meaning that when the third line is intersecting them both, the angles formed will be exactly the same. The top angle that is to the right is 25°, meaning that he bottom angle to the left is 25°. All that is left is to find the last two angles in order to find out what the answer to the equation is. The 25° angle is next to a triangle causing the lines to be flat, or 180°.

180 - 25 = 155

That means the bottom angle to the right is 155. In order to find x, subtract 10 and divide by 3.

3x + 10 - 10 = 155 - 10

3x = 135

3x/3 = 135/3

x = 48.3

6 0
2 years ago
Which is the graph of g(x) = x - 16?
kakasveta [241]

Answer: See attached graph

8 0
3 years ago
Read 2 more answers
You know that you want some type of wood flooring. You found these options at the store.
xenn [34]

Answer:

how much wood do you need

8 0
3 years ago
Other questions:
  • Write an equivalent equation that does not contain parentheses for 3(k-x) = -3x-9
    11·1 answer
  • What is the inverse of f(x) =1/3 x + 2?
    15·1 answer
  • Which is the equation of a line with a slope of -1 and a y-intercept of -6?
    14·1 answer
  • In golf your scores can be under or over par. If a golfer has 3 games in which he scores 3 under on the first, 5 over in the sec
    12·1 answer
  • The energy usage of a light bulb is a function. The input for the function is _____ measured in hours.
    11·1 answer
  • Silas took 17 bags of glass to the recycling center. He still has 8 bags of plastic to take to the recycling center. Which equat
    12·1 answer
  • Please help me with this!!!!
    12·1 answer
  • Use right triangle DCB to find the trig values for angle D <br>​
    6·2 answers
  • Convert 614 into base five number system.​
    14·1 answer
  • 5/9 rounded to the nearest thousand​
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!