Thursday

September 18, 2014

September 18, 2014

Posted by **Janet** on Sunday, May 8, 2011 at 11:34pm.

f(x)= ax^2+bx+c

Using calculus find the vertex of the parabola formed by this quadratic function. Determine under what conditions this vertex is a maximum or minumum (using Calculus techniques). Show work using derivatives to justify our conclusions.

THis is what I did so far, but can't figure out the rest.

f'(x)= 2ax + b

0=2ax+b

-b = 2ax

-b/2a = x

Please help and show steps so that I can understand.

- calculus -
**Damon**, Monday, May 9, 2011 at 6:19amThat is correct. The minimum ofr maximum (vertex) is at x = -b/2a

You already know that from the quadratic equation. x = -b/2a +/- (b/2a)sqrt (b^2-4ac)

Now

if x = -b/2a

what is y?

y = a (b^2/4a^2) + b(-b/2a) + c

= b^2/4a -b^2/2a + c

= -b^2/4a+c

for max or min

f" = 2 a

if a is +, that is a minimum

if a is -, that is a maximum

**Answer this Question**

**Related Questions**

Math: Parabola, Vertex - Find the vertex of the parabola associated with the ...

Algebra - I'm trying this again, I'd like the quadratic form, so i can then work...

algebra II - Can you please help me with the these problems. 8.Write an equation...

Algebra 1 parabola's - I have a graph with a parabola on it and asked to write ...

Algebra - Can you please help me with the following problems? Find the ...

College Algebra - A quadratic function has its vertex at the point (-9,8). The ...

Algebra Problems - Please check my answers. Find the coordinates of the vertex ...

Algebra - Please check my answers. Find the coordinates of the vertex for the ...

Algebra - Please check my answers. Find the coordinates of the vertex for the ...

Maths - It is given a quadratic function y=a(x-h)62+k.If its graph is a parabola...