To graph a quadratic equation, all you really need is the vertex (the minimum or maximum point) and the $x$-intercepts (if the quadratic has any). Thus, Graphing Quadratics by Factoring is actually quite straightforward if the quadratic equation is factorable.

How do we do it?

Step 1: If the quadratic equation is factorable, factor it. You can see an example below:

$$y = x^2 + 8x + 15$$

$$y = (x+3)(x+5)$$

Step 2: Set $y$ equal to $0$ to find the two $x$-intercepts.

$$0 = (x+3)(x+5)$$

$$x = -3, -5$$

Step 3: Find the vertex (the minimum $y$-value) by plugging in the $x$-value that is precisely between the two $x$-intercepts. In this case, our two $x$-intercepts are $-3$ and $-5$. The $x$-value right in the middle is $x = -4$. Plug it in to the original quadratic to get the minimum $y$-value (see below):

$$y = (-4)^2 + 8(-4) + 15$$

$$y = -1$$

Step 4: Graph the parabola. It's actually quite easy now that we have three points, the two $x$-intercepts and the vertex.

$x$-intercept$_1$: $(-3, 0)$

$x$-intercept$_2$: $(-5, 0)$

vertex (minimum value): $(-4, -1)$