1. ## The Parabola

Find (a) the directrix, (b) the focus, (c) the roots of the parabola y = x^2 -5x + 4.

I have never seen a parabola written that way.

2. Originally Posted by magentarita
Find (a) the directrix, (b) the focus, (c) the roots of the parabola y = x^2 -5x + 4.

I have never seen a parabola written that way.
You're probably used to seeing the quadratic written in vertex form like:

$y=a(x-h)^2+k$

$y = x^2 -5x + 4$

Now, just complete the square:

$y=\left(x^2-5x+\frac{25}{4}\right)-\frac{25}{4}+4$

$y=\left(x-\frac{5}{2}\right)^2-\frac{9}{4}$

Vertex $(h, k) = \left(\frac{5}{2}, -\frac{9}{4}\right)$

Directrix:

$y=k-\frac{1}{4a}$

Focus:

$\left(h, k+\frac{1}{4a}\right)$

Roots (zeros):

$x^2-5x+4=0$

Factor and solve for x.

3. ## ok.........

Originally Posted by masters
You're probably used to seeing the quadratic written in vertex form like:

$y=a(x-h)^2+k$

$y = x^2 -5x + 4$

Now, just complete the square:

$y=\left(x^2-5x+\frac{25}{4}\right)-\frac{25}{4}+4$

$y=\left(x-\frac{5}{2}\right)^2-\frac{9}{4}$

Vertex $(h, k) = \left(\frac{5}{2}, -\frac{9}{4}\right)$

Directrix:

$y=k-\frac{1}{4a}$

Focus:

$\left(h, k+\frac{1}{4a}\right)$

Roots (zeros):

$x^2-5x+4=0$

Factor and solve for x.
This is exactly what confused me. I thank you for making life easy here for me.