If a quadratic is not factorable, or even if it is (lol), you can use Graphing by Completing the Square. Let's do it with the example below:

$$y = x^2 -8x + 4$$

Notice how the equation above is NOT factorable.

Step 1: Complete the square. If you forgot how to do that, revisit that mountain entry in Algebra.

$$y = x^2 -8x + 4$$

$$y + 16 = x^2 -8x + 16 + 4$$

$$y + 16 = (x^2 -8x + 16) + 4$$

$$y + 16 = (x-4)^2 + 4$$

$$y = (x-4)^2 - 12$$

Step 2: Use the equation in which we completed the square to find the minimum value. That's easy. We know the $(x-4)^2$ is always going to be positive except in the case in which it's $0$. Let's make it $0$ by saying $x=4$. And when $x=4$, $y = -12$.

vertex (minimum value): $(4, -12)$

Step 3: Find two to four other points (to make graphing easier). I recommend moving one or two points to the left and right of the vertex. Let's see what happens when $x=3$ and when $x=5$. Hell, let's also see what happens when $x=2$ and $x=6$.

other point$_1$: $(3, -11)$

other point$_2$: $(5, -11)$

other point$_3$: $(2, -8)$

other point$_4$: $(6, -8)$

Step 4: Graph it.