Question

I'm having troubles understanding how to find the directrix,focus and roots of the parabola y=x^2-5x+4. If you could explain it to me so I understand for myself I'd appreciate it.

Answer 1

Y = x^2 - 5x + 4

h = Xv = -B/2A = 5/2 = 2.50 = Value of X
at the vertex.

k = 2.5^2 - 5*2.5 + 4 = -2.25 = Value of
Y at the vertex.

D(2.5,Y1), V(2.5,-2.25), F(2.5,Y2)
In a y-parabola, the y-coordinates vary
while the x-coordinates remain constant
and is equal to h(2.50).

The distance between the points equals
1/4a = 1/4 = 0.25.

-2.25 - Y1 = 0.25
Y1 = -2.50

Y2 - (-2.25) = 0.25
Y2 + 2.25 = 0.25
Y2 = 0.25 - 2.25 = -2.0

Solution or Roots:

4 = 1*4 = (-1)*(-4)
Select the pair of factors whose sum=B:
(-1) + (-4) = -5 = B.

x + (-1) = 0
x - 1 = 0
X = 1

x + (-4) = 0
x-4 = 0
X = 4

Solution Set:
(x,y) = (1,0), (4,0)
Both points should satisfy the given Eq.