Identify the maximum value of the function y = -6x^2-12x-1

Question

phi · Answer

your function is a parabola with a $ \cap $ shape.  the max value is at its vertex.
Can you find its vertex?

igreen · Answer

@phi is Correct.

You have to find the vertex.

anonymous · Answer

max value of the function will be 5
Reason:
find the 1st derivative and equate it to zero
and put that value in the expression you will get the max value of the function

igreen · Answer

First start off with $\dfrac{-b}{2a}$

igreen · Answer

This expression will give us the x-intercept of the vertex, then we can plug it back into the equation and get our y-intercept.

igreen · Answer

Our parabola is in the form of ax^2 + bx = c

-6x^2-12x-1

So in this case:

a = -6

b = -12

c = -1

anonymous · Answer

@iGreen best way to find the 1st derivative 
rather going for the intercept

igreen · Answer

Now we can plug in our terms into the expression:

$\dfrac{-b}{2a}$

$\dfrac{12}{2(-6)}$

$\dfrac{12}{-12}$

-1

igreen · Answer

Which gives us -1 as the x-value for the vertex.

Now we can plug in x = -1 into our parabola to get the y-intercept.

$y = -6x^2-12x-1$
$y = -6(-1)^2-12(-1)-1$
$y = -6(1)+12-1$
$y = -6+12-1$
$y = 6 - 1$
$y = 5$

So our vertex is (-1, 5).

igreen · Answer

@LilRob

anonymous · Answer

@iGreen got it thanks man

igreen · Answer

No problem.