Author Question: Someone please help me, who is good in math? (Read 2599 times)


  • Sr. Member
  • ****
  • Posts: 384
My homework is killing me.

What is the vertex of this function.
f(x)= (2p) x ^2 - (12p)x + (3p)


  • Sr. Member
  • ****
  • Posts: 324
check this for a typo in the last term

Related Topics

Need homework help now?

Ask unlimited questions for free

Ask a Question


  • Full Member
  • ***
  • Posts: 204
f(x) = (2p)x² - (12p)x + (3p)

First we need the axis of symmetry which is -b/2a with quadratics in the form of ax² + bx + c = 0

In your case, a = 2p and b = -12p

Therefore, your axis of symmetry is:

12p / 4p = 3

x = 3

Plug this x-value back into the equation:

f(3) = (2p)*3² - (12p)*3 + (3p)
f(3) = (18p) - (36p) + (3p)
f(3) = -15p


Your vertex is:

(3, -15p)


  • Hero Member
  • *****
  • Posts: 705
The x-coordinate of the vertex is given by the formula
x = -b/2a
so in this case,
x = -(-12p)/(2*2p)
x = 3

The y-coordinate can be found by finding what y is equal to for that value of x:
f(3) = 2p(3^2) - (12p)*3 + 3p
=18p - 36p + 3p

So the vertex is at the point (3, -15p).


  • Hero Member
  • *****
  • Posts: 705
It is a quadratic where the coefficients are factors of p instead of being "normal" numbers.

The vertex is a critical point: a maximum or minimum.  It is where the slope is equal to zero.

To find the slope, you can differentiate:

f(x) = 2p x^2 - 12p x + 3p
f'(x) = 2(2p)x - 12p
f'(x) = 4p(x) - 12p
f'(x) = 4p (x - 3)

Since p cannot be zero (otherwise your graph would be a flat line -- the x axis), then (x-3) must be zero, and that will only happen when x = 3

To find the vertex point, set x = 3 in the original equation:
f(x) = 2p x^2 - 12p x + 3p
f(3) = 2p(9) -12p(3) + 3p
f(3p) = 18p -36p + 3p = -15p

Vertex is at (x, f(x)) = (3, -15p)


  • Sr. Member
  • ****
  • Posts: 308
f(x) = 2px² - 12px + 3p
f(x) = 2p(x² - 6x ....) + 3p
f(x) = 2p(x² - 6x + 9) + 3p - 18p
f(x) = 2p(x - 3)² - 15p
vertex is (3, -15p)


Did you know?

More than 50% of American adults have oral herpes, which is commonly known as "cold sores" or "fever blisters." The herpes virus can be active on the skin surface without showing any signs or causing any symptoms.

Did you know?

Though the United States has largely rejected the metric system, it is used for currency, as in 100 pennies = 1 dollar. Previously, the British currency system was used, with measurements such as 12 pence to the shilling, and 20 shillings to the pound.

Did you know?

In Eastern Europe and Russia, interferon is administered intranasally in varied doses for the common cold and influenza. It is claimed that this treatment can lower the risk of infection by as much as 60–70%.

Did you know?

Normal urine is sterile. It contains fluids, salts, and waste products. It is free of bacteria, viruses, and fungi.

Did you know?

Blood is approximately twice as thick as water because of the cells and other components found in it.

For a complete list of videos, visit our video library