What is this math called and how to do it?

you're working with the graph in factored/x-intercept form, and you're doing it to find the points where the graph crosses the various axis, aka finding the zeros.

graphs cross the x-axis when they have no height, in other words when their partner in the point (x, y) equals 0.... So plug in y = 0 and solve for x

(x+3)(x+4)(x-1) = y

(x+3)(x+4)(x-1) = 0

since it's already in factored form, you just set each part equal to 0 and solve

(x+3) = 0 and (x+4) = 0 and (x-1) = 0

x + 3 = 0 and x + 4 = 0 and x - 1 = 0

x = -3 and x = -4 and x = 1

So you have zeros at (-3, 0), (-4, 0), and (1, 0).

You find the y-intercept when x has no value to the left or right, aka when x = 0. Plug that in and solve for y

y = (0+3)(0+4)(0-1)

y = (3)(4)(-1)

y = -12

So your y-intercept is at (0, -12)

x-intecepts are where the curve cuts the x-axis (y=0)

(x+3)(x+4)(x-1)=0

x+3=0

x=-3

(x+4)=0

x=-4

x-1=0

x=1

The curve cuts the x-axis at x=-3, y=0 and x=4, y=0 and x=1,y=0

(-3,0) ,(-4,0) and (1,0) are x-intercepts

y-intercepts are where the curve cuts the axis (x=0)

when x=0

y = (x+3)(x+4)(x-1)

when x=0

y = (0+3)(0+4)(0-1)

y= (3)(4)(-1) = -12

(0,-12) is the y-intercept

here's the graph of y = (x+3)(x+4)(x-1)

http://www.wolframalpha.com/input/?i=graph+of++y+%...

The x intercepts- where the function crosses the x axis- is where the function is zero. That's when any of the three brackets is zero- ie x is -3, -4 and 1.

Similarly, the y intercept is when x is zero. That's 3*4*-1 ie y = -12.

To draw a graph, use those points for a start, and then for other whole number values of x from (say) -5 to 2.