Question 1030328
What are the coordinates of the points where the graphs of f(x)=x^3-x^2+x+1 and g(x)=x^3+x^2+x-1 intersect? 
:
At intersection g(x) = f(x)
write it as one equation
x^3 + x^2 + x - 1 = x^3 - x^2 + x + 1
Combine like terms
x^3 - x^3 + x^2 + x^2 + x - x = 1 + 1
2x^2 = 2
divide by 2
x^2 = 1
x = +/-{{{sqrt(1)}}}
x = 1
and
x = -1
:
Find y when x = 1
y = 1^3 + 1^2 + 1 - 1
y = 2
:
Find y when x = -1
y = -1^3 + 1^2 -1 - 1
y = -1 + 1 - 1 - 1
y = -2
:
Two coordinates: -1,-2; 1,2
:
looks like this
{{{ graph( 300, 300, -3, 3, -4, 4, x^3-x^2+x+1,x^3+x^2+x-1) }}}