GRAPHING QUADRATICS USING THE INTERCEPTS

The easiest way to find the intercepts is through factored form as you already have the two x-intercepts, now here is how you find the rest of the graphing components.

First, Once you have recieved your final answer (which it's signs have been already switched) You have finshed finding your x-intercepts. you can call these intercepts the "roots" as well (Roots=0).

(x-4)(x+12)

Into

(4,0),(-12,0)

Second, to find the "axis of symmetry" (a.o.s) you would take your two answers that were switched from "r" and "s". Finally you would first add them and after divide them by 2 as the (a.o.s) represents the mid-point of your parabola.

Third you have completed your first part of the vertex but you still need to find the optimal value. What you need to do is you substitude your (a.o.s) into your x-intercepts to recieve you "y" for your vertex.

(-12+4)/2 = -4

(You can punch this whole equation in your "scientific caculator" but make sure you have brackets between the two numbers you are adding so your caculator can caulate your expression through "Bedmas" adding the two numbers first and dividing by "2" second, and you don't recieve a different answer)

or (a.o.s)

(-4-4)(-4+12)=-64

GRAPH

Finally, you have all of the graphing components and all you have to do is graph this equation.

Vetex (4,-64)
Roots = (-12,0) (4,0)
opitimal value: y = -64
Axis Of Symmetry: x = -4

(-12,0,)

(4,0,)

a.o.s x = (-4,0,)

Vertex = (-4,-64,)