Step-by-step explanation:
So, let's use x2 - 3x - 28 as an example.
It's factors are (x - 7)(x + 4).
The roots are the x-values that make our expression equal 0. In order for x2 - 3x - 28 to equal 0, either of our factors need to equal 0, since 0 times anything is 0.
x2 - 3x - 28 = 0
(x - 7)(x + 4) = 0
x - 7 = 0
x = 7
(7 - 7)(7 + 4) = 0(11) = 0
x + 4 = 0
x = -4
(-4 - 7)(-4 + 4) = -11(0) = 0
That gives us two points on our graph, (7,0) and (-4,0). Where are those? On the x-axis! Thus, there are our x-intercepts.
By the way, for the future, along the x-axis, y = 0, so if you are asked for the x-intercepts (or roots), set y = 0 and solve for x.
Along the y-axis, x = 0, so if you are asked for the y-intercepts, set x = 0 and solve for y.
y = 02 - 3(0) - 28
y = -28
So, the y-intercept(s) of our same equation is y = -28, or (0,-28).
Boom.
