perfect square questions

[Guest]

How do you do this?

Find the max or min value of each function and the value of x when it occurs.

y= -4x^2 - 8x +5

Solve by completing the square.
5x^2-2x+2=0

 

[tkhunny]

How do you do this?

Your instructions suggest completing the square. Why not do that?

y= -4x^2 - 8x +5
y = -4(x^2 + 2x + _______ - _______) + 5

2/1 = 1
1^2 = 1

y = -4(x^2 + 2x + 1 - 1) + 5
y = -4(x^2 + 2x + 1) - (-4)(1) + 5
y = -4(x + 1)^2 + 4 + 5
y = -4(x + 1)^2 + 9

x-value where min or max is achieved? x + 1 = 0 or x = -1
min or max value? 9
Min or max? -4 < 0, so this is a maximum

Check by secret formula. -b/2a = -(-8)/2*(-4) = 8/(-8) = -1 That's not a coincidence.

 

[Guest]

I don't get how you made this 5x^2-2x+2=0 a perfect square..in the text they have imaginary numbers used ( i ) they gave 2 corrdinates

 

[tkhunny]

Solve by completing the square.
5x^2-2x+2=0

Well, complete the square.

5x^2-2x+2=0
5(x^2-(2/5)x+________-______)+2=0

(2/5)/2 = (1/5)
(1/5)^2 = 1/25

5(x^2-(2/5)x+(1/25)-(1/25))+2=0
5*(x^2-(2/5)x+(1/25))-5*(1/25)+2=0
5*(x-(1/5))^2 - (1/5)+2=0
5*(x-(1/5))^2 + (9/5)=0
5*(x-(1/5))^2 = -(9/5)
(x-(1/5))^2 = -(9/25)
x - (1/5) = sqrt(-9/25) or (x - 1/5) = -sqrt(-9/25)
x = (1/5) + (3/5)i or x = (1/5) - (3/5)i