Find x Intercepts of the Functions

Find x Intercepts of the Functions.

(1) y = x^2(x - 4)(x + 2)


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

To find x-intercepts, let y = 0 and apply the zero product property.

1.
y = x^2 (x - 4)(x + 2)
x^2 (x - 4)(x + 2) = 0 iff
x^2 = 0 or x - 4 = 0 or x + 2 = 0 iff
x = 0 or x = 4 or x = -2

Thus x-intercepts are (0, 0), (4, 0), and (-2, 0).

2.
y = -3x^2 (x + 1)^4 iff
-3x^2 = 0 or (x + 1)^4 = 0 iff
x^2 = 0 or x + 1 = 0 iff
x = 0 or x = -1

Thus x -intercepts are (0, 0) and (-1, 0).

guitar: When you expand (1) you end up with X^4-2X^3-8X^2. If we set X as 0; the X intercept, we find that Y also will equal0 ;Therefore the X inter4cept will be (0,0) Since (2) has this same characteristic, it too will hace an X intercept of (0,0) In order for it to be different, Y equal must have at least 1 constant. You functions do not.

The x intecepts are when y = 0
That happens when any factor = 0.

Since everything is factored in you problems, set each factor to zero and solve for x
1)x^2 = 0 when x = 0
(x - 4) = 0 when x = 4
(x + 2) = 0 when x = - 2

2) - 3x^3 = 0 when x = 0
(x + 1)^4 = 0 when x = -1

1) (-2,0) (0,0) (4,0)
2) (-1,0) (0,0)

x^2(x - 4)(x + 2)=0
x^2=0; x-4=0; x+2=0
x=0; x=4; x=-2

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