what is the vertex of the function, s=p^2+120p+1400?

Answer 1

Hey there!

Use Completing the Square Formula.

s=p^2+120p+1400 -->
s-1400=p^2+120p -->
s-1400+(120/2)^2=p^2+120p+(120/2)^2 -->
s-1400+60^2=(p+60)^2 -->
s-1400+3600=(p+60)^2 -->
s+2200=(p+60)^2 -->
s=(p+60)^2-2200

So s=(p+60)^2-2200 is the vertex form of the parabola.

The vertex form of the parabola is y=(x-h)^2+k.

Since h=-60 and k=-2200, the vertex (h,k) is (-60,-2200)

Hope it helps!

*Who's putting all the thumbs-down for the correct answers?*

Answer 2

Method 1(differentiation)
s (p) = p² + 120 p + 1400
s `(p) = 2p + 120 = 0 for turning point
p = - 60
3600 - 7200 + 1400 = - 2,200
V (- 60, - 2,200)

Method 2 (completing square)
s = ( p ² + 120 p + 3600 ) - 3600 + 1400
s = ( p + 60 ) ² - 2200
s = [ p - ( - 60 ) ] ² - 2200
V (- 60 , - 2,200) as above

Answer 3

p^2 +120 p + 1400 = (p+60)^2 - 2200

Hence the vertex is located at (-60, -2200).


EDIT Who's that usurper?

Answer 4

To find the p coordinate of the vertex of a quadratic function,
f(p) = ap^2 + bp + c, you can use the formula:

p=-b/2a

(this comes from the quadratic formula...you will have to trust me)

In your case a=1, b=120, and c =1400

so if you substitute for b and a you get

p= -(120)/2(1)

p= -60

Then plug the value of x into the original equation, s=p^2...

and get s=-2200

so the vertex is (-60,-2200)

this answer makes sense because the graph of the original function is a parapola that opens upwards, making the vertex the minimum point on the graph.

Hope this helps

Answer 5

The vertex is at the point (h, k), where h represents -b / (2a) and k represents c - b^2 / (4a).

From this we say:

h = -b/2a, where b represents the coefficient of the p term and a represents the coefficient of the p^2 term.

Let's find h first and then we can find k.

By the way, c = 1400 in your fuction. We will need 1400 later to find k.

Seeking for h:

h = -b/2a

h = -(120)(2)(1)

h = -120/2

h = -60

We now need to look for k.

Seeking for k:

k = c - b^2 /(4a).

k = 1400 - (120)^2/(4)(1)

k = 1400 - 14400/4

We must divide -14400 by 4 before subtraction.

Recall the PEMDAS rules, right?

k = 1400 - 3600

k = -2200

The vertex is the point (-60, -2200).

Done!

Answer 6

The easiest way is to use the vertex formula. The vertex is at the point (h, k) where

h = -b / (2a)
k = c - b^2 / (4a)

a = coefficient of x^2
b = coefficient of x
c = constant term

In this case,
a = 1
b = 120
c = 1400

so we have
h = -120 / (2 * 1) = -60
k = 1400 - 120^2 / (4 * 1)
= 1400 - 14400 / 4
= 1400 - 3600
= -2200

So the vertex is the point (-60, -2200)

Hope this helps.

Answer 7

roots are :

-106.9042
-13.0958

Answer 8

The vertex is the point where the derivative is zero. The derivative of this function is 2p + 120. So

2p + 120 = 0
2p = -120
p = -60

That's the value of p. To find the value of f(p), substitute in the original equation:

f(-60) = (-60)^2 + 120(-60) + 1400 =
3600 -7200 + 1400 = -2200

So the point at the vertex is (-60,-2200)

Answer 9

formula Vx = (b/2a)

A = 2
B = 120
C = 1400

plug em in!