Question

use the graph of $y = x^2 - x - 2$ to find the solutions of $x^2 - x - 2 = 0$.
$x =$ select choice or $x =$ select choice

Explanation:

Step1: Understand the problem

We need to find the solutions of the quadratic equation \(x^{2}-x - 2=0\) using the graph of \(y=x^{2}-x - 2\). The solutions of the equation \(ax^{2}+bx + c = 0\) are the \(x\)-intercepts (where \(y = 0\)) of the graph of \(y=ax^{2}+bx + c\).

Step2: Identify the x - intercepts from the graph

Looking at the graph of \(y=x^{2}-x - 2\), we observe the points where the parabola intersects the \(x\)-axis. From the grid - like graph, we can see that the parabola intersects the \(x\)-axis at \(x=- 1\) and \(x = 2\). We can also verify this by factoring the quadratic equation: \(x^{2}-x - 2=(x - 2)(x+1)\). Setting \((x - 2)(x + 1)=0\), we get \(x-2=0\) or \(x + 1=0\), which gives \(x = 2\) or \(x=-1\).

Answer:

\(x=-1\) or \(x = 2\)