SOLUTION: Identify the coordinates of the vertex and focus, the equations of the axis of symmetry and directrix, and the direction of opening of the parabola with equation y = 2x 2 - 4x

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Identify the coordinates of the vertex and focus, the equations of the axis of symmetry and directrix, and the direction of opening of the parabola with equation y = 2x 2 - 4x      Log On


   

Question 1176544: Identify the coordinates of the vertex and focus, the equations of the axis of
symmetry and directrix, and the direction of opening of the parabola with
equation y = 2x
2 - 4x + 5.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi

the vertex form of a Parabola opening up(a>0) or down(a<0), 
y=a%28x-h%29%5E2+%2Bk 
where(h,k) is the vertex  and  x = h  is the Line of Symmetry , 
the focus is (h,k + p), With Directrix y = (k - p), a = 1/(4p)

y = 2x^2 - 4x + 5 = 2(x-1)^2 -2 + 5 = 2(x-1)^2 +3
 y = 2(x-1)^2 +3
a = 1/(4p) 0r p = 1/4a = 1/8

  V(1,3)  and x = 1 is the Line of Symmetry 

 F( 1, 3.125)   Directrix y = 3 - .125) = 2.875
Wish You the Best in your Studies.