f(x) = 2x^3 − 10x^2 + 12x

Question

 Plot sufficient solution points.

x
0
1
2
2.5
3
3.5
4

Answer 1

f(x) =2x^3 -10x^2 + 12 = 2x(x^2 -5x +6) = 2x(x-3)(x-2)

f(0) = 0, the origin is an x intercept

f(1) = 4

f(1.5) = 9/4 = 2.25

f(2) = 0, 2 = 2nd x intercept

f(2.5) = -5/4 = - 1.25

f(3) =0, 3 = 3rd x intercept

f(3.5) = 21/4 = 5.25

f(4) = 16

(0,0), (1,4), (1.5, 2.25), (2,0), (2.5, -1.25), (3,0), (3.5, 5.25), (4,16)