quadratics and parent functions?

[curlz]

1. How would I solve the using the quadratic formula? 4x² - 12x + 7 = 0

2. What would be the equation of the quadratic function with zeroes 2 and 6 and a vertex at (4,4)

3. With the parent function y = x² what would be the equation that shift the function 5 units right and 3 units up?

4. With the parent function y = ?x what would be the equation that vertically stretch the function by a factor of 5 and it 4 units down?

[aero]

1.- x= (12 +- sqrt (144-112))/8        x= (12+- sqrt(32))/8    

2.- a parabola  (Simetrical w/respect Y axis) )   y-k =4p(x-h)^2       (h,k )  vertex   , p focus distance
     y-4 =4p(x-4) ^2         if  x=2    y=0    ,  -4=4p(2-4)^2   ,   p= - 1/4
     y-4= -1(x-4)^2    since p<0  parabola has arms down .-

3.- Y=X^2    has vertex in (0,0)    .- You must shift the vertex coodinates 5 y 3
     Y-3 = (X-5 ) ^2      .-  

4.- Y^2 =X    ( Horizontal parabola )     It has the general form
        (y-k)^2 =4p ( x-h)  
If you want  to close it arms you must act on p  .- in your case 4p=1  or  p=1/4  
If you want close p 5 times  then p=(1/4 ) /5  =1/20   and 4p= 1/5

   (Y-0)^2 = 1/5 (X-0)       ,  Y^2= 1/5 X