Chapter 2.1, Problem 47E

To determine

To find the x -intercept of the given graph of function $y=x^2-2x-3$ , also find x -intercept algebraically.

Answer to Problem 47E

Explanation of Solution

Given:

Graph of function $y=x^2-2x-3$

  

Concept Used:

The x -intercept of a function $f\left(x\right)$ are the points where its graph intersect x- axis. Algebraically x- intercept can be found by putting

  $f\left(x\right)=0$

Calculation:

To find the x -intercept of the given graph of function $y=x^2-2x-3$ note the points where it cuts the x- axis.

Note that the graph of the function $y=x^2-2x-3$ intersect x -axis at points $-1,\text{ and 3}$ .

Thus, x -intercepts of given function are $x=-1,\text{ and }x=\text{3}$

Now, to find x -intercepts algebraically find values of x where $f\left(x\right)=0$ . As

  $\begin{array}{c}f\left(x\right)=0\\ \Rightarrow y=x^2-2x-3=0\\ \Rightarrow x^2-3x+x-3=0\\ \Rightarrow x\left(x-3\right)+\left(x-3\right)=0\\ \Rightarrow \left(x+1\right)\left(x-3\right)=0\\ \Rightarrow x=-1,\text{ and }x=3\end{array}$

Thus, $x=-1,\text{ and }x=3$ are x -intercepts of given function.