SOLUTION: please help me with this problem . Find (a)the directrix (b)the focus and (c)the roots of the parabola y=x^2-5x+4 (x^2 is x squared) thanks

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: please help me with this problem . Find (a)the directrix (b)the focus and (c)the roots of the parabola y=x^2-5x+4 (x^2 is x squared) thanks       Log On


   

Question 33567: please help me with this problem .
Find (a)the directrix (b)the focus and (c)the roots of the parabola y=x^2-5x+4 (x^2 is x squared) thanks
Answer by mukhopadhyay(490) About Me  (Show Source):
You can put this solution on YOUR website!
y=x^2-5x+4
=> y = (x-5/2)^2+4-25/4
=> y = (x-5/2)^2 - 9/4;
=> (x-5/2)^2 = 4(1/4)(y+9/4)
The vertex of the parabola is at (5/2, -9/4)
The directrix is at y = (-9/4-1/4) => y = -10/4 = > y = -5/2
The focus is at (5/2, -9/4+1/4) = (5/2, -2);