Author Question: Someone please help me, who is good in math? (Read 2981 times)

j_sun

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

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



hummingbird

  • 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

Melanie

  • 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)



camila

  • 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)
=12p/4p
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
=-15p

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



camila

  • 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)



federox

  • 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?

Nearly all drugs pass into human breast milk. How often a drug is taken influences the amount of drug that will pass into the milk. Medications taken 30 to 60 minutes before breastfeeding are likely to be at peak blood levels when the baby is nursing.

Did you know?

GI conditions that will keep you out of the U.S. armed services include ulcers, varices, fistulas, esophagitis, gastritis, congenital abnormalities, inflammatory bowel disease, enteritis, colitis, proctitis, duodenal diverticula, malabsorption syndromes, hepatitis, cirrhosis, cysts, abscesses, pancreatitis, polyps, certain hemorrhoids, splenomegaly, hernias, recent abdominal surgery, GI bypass or stomach stapling, and artificial GI openings.

Did you know?

Serum cholesterol testing in adults is recommended every 1 to 5 years. People with diabetes and a family history of high cholesterol should be tested even more frequently.

Did you know?

Multiple sclerosis is a condition wherein the body's nervous system is weakened by an autoimmune reaction that attacks the myelin sheaths of neurons.

Did you know?

The largest baby ever born weighed more than 23 pounds but died just 11 hours after his birth in 1879. The largest surviving baby was born in October 2009 in Sumatra, Indonesia, and weighed an astounding 19.2 pounds at birth.

For a complete list of videos, visit our video library