What is the axis of symmetry for f(x) = −3x2 + 12x − 6?

Question

22-06-2017
Mathematics

contestada

What is the axis of symmetry for f(x) = −3x2 + 12x − 6?

Respuesta :

Otras preguntas

Greg wants to find the median of a set of 9 data items.First,he ordered the items from least to greatest.What should he do next?

The nodules that serve as an important habitat for marine life are what?

A(n) ____________ should have only one independent variable.

Compare and contrast procedures in a criminal case with procedures in a civil case.

What is the area, rounded to the nearest tenth of square inch, of an equilateral triangle that has a perimeter of 24 inches? Area = square inches

Shaky hands before a test Test anxiety Relaxation Visualization Preparing your body Preparing your mind Positive self-talk

A muscle inserts 1.5 cm from the joint axis and exerts 300 N of force at an angle of pull of 60 degrees. How much torque is produced by this muscle? In your wor

Convection heat transfer mode is comprised of which of the following mechanism? Select one: O a. Energy transfer solely due to macroscopic motion of fluid O b.

In the extraction of aluminium from bauxite ore, several steps are involved. In one of these, sodium hydroxide (NaOH) reacts with aluminium oxide (Al2O3) to pro

Find (f-g)(x) for the following functions. f(x) = –12x3 + 19x2 – 5 g(x) = 7x2 + 15

irspow irspow · Answer 1 · 2017-06-22T20:09:31+02:00

The axis of symmetry can be found by finding the average of the zeros, a derivation from the conservation of energy :P, or by finding the point when the velocity is equal to zero.

df/dx=-6x+12 so df/dx, velocity, equals zero when:

-6x+12=0

6x=12

x=2 so the axis of symmetry is the vertical line x=2

....

average of zeros...

3x^2-12x+6=0

x^2-4x+2=0

x^2-4x=-2

x^2-4x+4=2

(x-2)^2=2

x-2=±√2

x=2±√2 so the average of the zeros is obviously 2.

....

conservation of energy

vf-vi=at When vf=0, this is the maximum value for f(x)...

-vi=at, vi=b and a(acceleration)=2a(from quadratic) and t=x

-b=2ax

x=-b/(2a) in this case

x=-12/(2(-3))

x=-12/-6

x=2

ColinJacobus ColinJacobus · Answer 2 · 2019-03-25T18:36:30+01:00

Answer: The axis of symmetry is [tex]x=2.[/tex]

Step-by-step explanation: The given function is

[tex]f(x)=-3x^2+12x-6~~~~~~~~~~~~~~~~(i)[/tex]

We know that for the function [tex]f(x)=a(x-h)^2+k,[/tex] the axis of symmetry is given by

[tex]x=h.[/tex]

From equation (i), we have

[tex]f(x)=-3x^2+12x-6\\\\\Rightarrow f(x)=-3(x^2-4x)-6\\\\\Rightarrow f(x)=-3(x^2-4x+4)+12-6\\\\\Rightarrow f(x)=-3(x-2)^2-6.[/tex]

Therefore, the axis of symmetry for the given function is

[tex]x=2.[/tex]

Also, the graph of the function is shown in the attached figure. It is a parabola with vertex (2, 6) and axis of symmetry x = 2.