Question

1. Given the relation y = x3 – x2 - 4x + 4, identify the x- and y-axis intercepts.

Answer 1

SOLUTION

Write out the equation for the relation

$y=x^3-x^2-4x+4$

The X-intercept is the value of x when y is equated to zero

hence if Y=o, the equation will be

$x^3-x^2-4x+4=0$

Then, using factor method

Substitute x=1 into the equation

$\begin{gathered} x=1 \\ (1)^3-(1)^2-4(1)+4=1-1-4+4=0 \\ \text{Hence} \\ (x-1)\text{ is a factor} \end{gathered}$

Similarly,

$\begin{gathered} \text{if x=2} \\ (2)^3-(2)^2-4(2)+4=8-4-8+4=0 \\ \text{hence } \\ (x-2)\text{ is a factor } \end{gathered}$

Similarly,

$\begin{gathered} \text{if x=-2, substitute into the equation } \\ (-2)^3-(-2)^2-4(-2)+4=-8-4+8+4=0 \\ \text{hence } \\ (x+2)\text{ is a factor} \end{gathered}$

Therefore, the factored form of the equation is

$\begin{gathered} \mleft(x-1\mright)\mleft(x+2\mright)\mleft(x-2\mright)=0 \\ x-1=0,x+2=0,x-2=0 \\ x=1,x=-2,x=2 \end{gathered}$

Then the x-intercepof the relation given is

$(1,0),(2,0)\text{ and (-2,0)}$

The Y-intercept is the value of Y when x is zero

$\begin{gathered} \text{if x=0} \\ y=x^3-x^2-4x+4 \\ y=(0)^3-(0)^2-4(0)+4 \\ y=4 \end{gathered}$

Hence, the Y-intercept is (0,4)

Therefore

x-intercept is (-2,0), (1,0), (2,0), and Y-intercept is (0,4)

The Last option is Correct (D)