Helppppp!7

Question

Sketch 3 different graphs that show you know the different number of x intercepts that are possible for a cubic function.

Answer 1

The x - intercepts of a Cubic Function is a solutions of the Cubic Functions.

X intercepts are the points where y = 0.

Let us Consider three cubic functions as

x³-6x²+11x-6 = 0

4x³-4x²+x = 0

4x³+4x² = 0.

Now Let us Consider the Equation x³-6x²+11x-6 = 0

Graph the Function x³-6x²+11x-6 = 0

Therefore x - intercepts of x³-6x²+11x-6 = 0 are 1 , 2 and 3.

Now Let us Consider the Equation 4x³-4x²+x = 0

x(4x²-4x+1) = 0

x (4x² -2x -2x + 1) =0

x ( 2x(2x - 1) -1 ( 2x - 1)) = 0

x (2x - 1)² = 0

Therefore x = 0, 0.5 and 0.5

Graph the Function4x³-4x²+x = 0

Therefore x - intercepts of 4x³-4x²+x = 0 are 0, 0.5 and 0.5.

Now Let us Consider the Equation x³+4x² = 0.

x²(x+4) = 0

Therefore x = 0, 0 and -4

Graph the Function x³+4x² = 0.

Therefore x - intercepts of x³+4x² = 0 are 0, 0 and -4.

Therefore graph of three cubic function is drawn having different x - intercepts.