Question 162445
Use the quadratic equation to get the roots


*[invoke quadratic "x", 1, -5, 4]

In order to find the vertex point you need to complete the square. You take the middle term half it and then square it.

y=x^2 - 5x + 4

Subtract 4 from each side

y-4=x^2 - 5x   take -5 and divide by 2   -5/2 and then square this term 25/4

y-4+25/4=(x-5/2)^2

y-16/4+25/4=(x-5/2)^2
y+9/4=(x-5/2)^2

Subtract 9/4 from both sides

y=(x-5/2)^2 -9/4

The vertex o=is (5/2,-9/4)

We know that since a is positive the parabola is facing upward

the directrix is below the vertex at distance -c on the x axis

the focus is a distance +c above the vertex

a=coefficient on x^2 term

It is 1  The equation for determining the c value is a=1=1/4c



4c=1

c=1/4

Y value for vertex+1/4= Focus, x value for vertex

the directrix is a line y=8/4=2