Simple Quadratic Factor question

[james_rich]

okay i need to solve the quadratic y = -x^2 + 5x + 6 and need to find the coordinates of the vertex of the curve

by factorising

y = -(x^2 - 5x - 5)
y = -(x + 1)(x - 6)

so when y = 0, x = -1 and x = 6 (that parts simple)
..............
At the vertex x = (-1 + 6) / 2 = 5/2 (as the curve is symetrical)

so as y = -x^2 + 5x + 6

y = -5/2^2 + 5(-5/2) + 6
y = 25/4 + 50/4 + 24/4
y = 99/4

(this is the answer i got which doesn't look right, and answer book gives a different answer)

can u tell me where i went wrong? thanx

 

[james_rich]

Sorry, this sites changed a bit since i last came on, I've posted it in the wrong section

 

[mathman]

y = -5/2^2 + 5(-5/2) + 6
y = 25/4 + 50/4 + 24/4

First line should read -(5/2)^2+5(5/2)+6
Second line should read -25/4+50/4+24/4
Result y=49/4
I suggest you carefully check your arithmetic before posting.

 

[james_rich]

thanx i got that answer too, wasn't sure which way to work it out, the negative sign threw me a bit, the book is wrong then as i thought, they have 29/4 for their answer!

thanx for ur help

 

[OvenMaster]

mathman is right & here's why:
-5/2*5/2=-25/4 because -1*1=-1
5 * 5/2 = 25/2 = 50/4
6 = 24/4
50 + 24 - 25 = 50 - 1 = 49/4
There's your answer

 

[HallsofIvy]

You can also do this by completing the square:
y= -x²+ 5x+ 6= -(x²- 5x)+ 6
= -(x²- 5x+ 25/4- 25/4)+ 6
= -(x- 5/2)²+ 25/4+ 6
= -(x- 5/2)²+ 25/4+ 24/4
= -(x- 5/2)²+ 49/4

The vertex is at (5/2, 49/4).