Find b and c so that the parabola http://webwork.rutgers.edu/webwork2_...bd38306ee1.png has vertex http://webwork.rutgers.edu/webwork2_...cbc6230861.png.

What do I do here?

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- Sep 21st 2011, 06:31 AMhabibixoxFinding the vertex at a given point?
Find b and c so that the parabola http://webwork.rutgers.edu/webwork2_...bd38306ee1.png has vertex http://webwork.rutgers.edu/webwork2_...cbc6230861.png.

What do I do here? - Sep 21st 2011, 06:34 AMSironRe: Finding the vertex at a given point?
Use completing the square:

Convert to

Where are the coordinates of the vertex. - Sep 21st 2011, 06:39 AMSudharakaRe: Finding the vertex at a given point?
- Sep 21st 2011, 03:05 PMhabibixoxRe: Finding the vertex at a given point?
wait so is it

x^2-18x+91? - Sep 21st 2011, 03:07 PMhabibixoxRe: Finding the vertex at a given point?
using the second method the derivative is

-8x + x right?

set that = 0

0= -8x + x

0= X(-8+1)

so final answer is 0? - Sep 21st 2011, 03:22 PMhabibixoxRe: Finding the vertex at a given point?
nvm b = 72 now im working on c ill get it :) i understand it...

- Sep 21st 2011, 06:18 PMSudharakaRe: Finding the vertex at a given point?
- Sep 21st 2011, 10:29 PMSironRe: Finding the vertex at a given point?
The method I was thinking about is the following.

Given is the parabola: and the vertex point with coordinates

In general we know we can directly read the coordinates of the vertex of a parabola if we convert to:

where are the coordinates of the parabola.

First, divide every term by so:

Use completing the square in the RHS:

That means:

(1) (1)

(2) (2)

Substituting (1) in (2) gives:

Therefore the parabola with vertex is:

But as you see, the method sudharaka wants to use is easier.