Answer to Question #152863 in Calculus for O.Weerasinghe

Question

y=|x²-2x-3| Solve the problem with the steps and draw the chart

Answer 1

$$y=|x^2-2x-3|$$

$$y=|(x+1)(x-3)|$$

$$y=0=>(x+1)(x-3)=0$$

$$=>x+1=0 \ \text {or}\ x-3=0$$

$$x_1=-1, x_2=3$$

$x^2-2x-3\geq0$ for $x\leq-1$ or $x\geq3$

$x^2-2x-3<0$ for $-1<x<3$

Therefore

$$y = \begin{cases} x^2-2x-3 &\text{if } x\leq-1 \\ -(x^2-2x-3) &\text{if } -1<x<3 \\ x^2-2x-3 &\text{if } x\geq3 \end{cases}$$