f(x)= -3x^2(x-2)(x+3)^2

Find the Leading term of f:

Find the x-intercept of f and their multiplicities:

Find the y-intercept of f:

Graph:

Question

f(x)= -3x^2(x-2)(x+3)^2

Find the Leading term of f:

Find the x-intercept of f and their multiplicities:

Find the y-intercept of f:

Graph:

campbell_st · Answer

so there are several ways to do this... 

the expansion of (x + 3)^2 is x^2

so the leading term is 

-3x^2 *x*x^2 = 

the x- intercepts... 

set it equation to zero 

$$-3x^2(x -2)(x + 3)^2 = 0$$

find the 3 values of x that make the equation true

its simple a case of solving the 3 equations

$$-3x^2 = 0,  x - 2 = 0  ~~and~~~x+3 = 0$$

the degree of the factor determines multiplicity...

campbell_st · Answer

use this sit https://www.desmos.com/calculatore to graph it... remember an even degree or multiplicity the curve only touches the x- axis

anonymous · Answer

Do I graph it using the original function?

campbell_st · Answer

yes... just type the equation in as you've written it

campbell_st · Answer

oops missed part of the address https://www.desmos.com/calculator