Question

How do you find the x-intercept of a cubic graph? For example y=2x^3+2, also, how does the 2 in front of the x influence the graph when compared to having a one in front?

Answer 1

x-intercept is a point on the curve where it crosses the x-axis, thus y = 0. substituting,
y = 2x^3 + 2
0 = 2x^3 + 2
0 = x^3 + 1
0 = (x + 1)(x^2 - x + 1)
thus the only real solution is
x = -1 ; and the x-intercept is at
(-1, 0)

for the second question, when the numerical coefficient of x^3 increases, the graph becomes narrower.

hope this helps :)

Answer 2

Thanks, that was really helpful :)