Express 2x² - 12x + 23 in the form a(x+b)² +c?

how would i sketch the curve y=2x² - 12x + 23


how would i find the points





plzz help mee...im confused!





tanx

Express 2x² - 12x + 23 in the form a(x+b)² +c?
Factor 2 out of the terms involving x





2(x^2 - 6x) + 23





Add and subtract the square of half of 6. (9)





2(x^2 - 6x + 9 - 9) + 23





take the subtracted 9 out of the brackets, remembering that it is multiplied by 2.





2(x^2 - 6x + 9) + 23 - 2(9)





Factor the trinomial in brackets. You can do this easily because it is a prefect square.





2(x-3)(x-3) + 23 - 2(9)





Simplify





2(x-3)^2 + 5
Reply:2(x² - 6x + 23/2)


2(x² - 6x + 9 - 9 + 23/2)


2(x² - 6x + 9) - 18 + 23


2(x - 3)² + 5


y = 2(x - 3)² + 5





Points on curve


(3 , 5) , (0 , 23) , (4 , 7)





(3,5) is a minimum turning point.





line x = 3 is an axis of symmetry


cuts y axis at y = 23


Does not cut x axis.
Reply:a generic way of converting would be





for mx^2 + nx + p = m(x + n/2m)^2 + (c-n^2/4m^2)
Reply:y = 2(x^2 - 6x + 11.5)


y = 2(x-3)^2 + 5
Reply:2x^2 - 12x + 23





take 2 as factor out





2(x^2 - 6x + 23/2)





complete the square





=%26gt;2[(x^2 - 2(3) x + 3^2 - 3^2 +23/2)]





=%26gt;2[(x - 3)^2 - 9 + 23/2)]





=%26gt;2[(x-3)^2 +5/2]





=%26gt;2(x-3)^2 + 5
Reply:express 2x² - 12x + 23 in the form a(x+b)² +c?





2x² - 12x =2(x^2 -6x)





let's make x^2-6x as a square of (x-3)


(x-3)^2 = x^2 -6x +9





so x^2-6x can be written as (x-3)^2 -9





2x² - 12x = 2(x-3)^2 -18





2x² - 12x + 23 = 2(x-3)^2 -18 +23 =


2(x-3)^2 +5





hence a =2; b =-3 and c =5
Reply:put in the form (ax+b)^2+c=a^2x^2+2abx+(b^2+c)


equate coefficients of x %26gt; 2x^2- 12x + 23


Then a^2=2, or a=rt(2), 2ab=-12 or b=-3rt(2), and b^2+c=23 or c=5.


%26gt;(rt(2)x-3rt(2))^2+5 or 2(x-3)^2+5


Curve has a min TV at (3,5), it's a parabola, plot it on a grafix calculator, or on a grid and put in values of x, say 1,2,3..etc and calculate y-values in 2(x-3)^2+5 for example.


Getting deja-vu here?! There is a formula for any quadratic you know...!
Reply:2 x^2 - 12 x + 23


= 2 [ x^2 - 6 x + 23/2 ]


= 2 [ x^2 - 6 x + 3 ^2 - 3^2+ 23/2 ]


= 2 [ (x - 3)^2 - 9 + 23/2 ]


= 2 [ (x - 3)^2 - 18/2 + 23/2 ]


= 2 [ (x - 3)^2 + 25/2 ]


= 2 (x - 3)^2 + 25