# Solve #x^2-x-2=0# graphically, by first sketching #y=x^2#?

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To solve the equation (x^2 - x - 2 = 0) graphically, we first sketch the graph of (y = x^2), which is a parabola.

Now, let's plot the graph of (y = x^2). This is a simple quadratic function, and its graph is a parabola that opens upwards.

To sketch the graph, we'll plot a few points and then connect them to get the shape of the parabola. We choose a range of x-values and calculate the corresponding y-values by squaring each x-value.

Let's take some arbitrary x-values, say -2, -1, 0, 1, and 2:

When (x = -2), (y = (-2)^2 = 4) When (x = -1), (y = (-1)^2 = 1) When (x = 0), (y = (0)^2 = 0) When (x = 1), (y = (1)^2 = 1) When (x = 2), (y = (2)^2 = 4)

Plotting these points, we get (-2, 4), (-1, 1), (0, 0), (1, 1), and (2, 4). Connecting these points gives us a parabola that opens upwards.

Now, to solve (x^2 - x - 2 = 0) graphically, we need to find the points where the graph of (y = x^2) intersects the x-axis. These points represent the solutions to the equation (x^2 - x - 2 = 0), where the curve intersects the x-axis.

We'll look for the x-values where (y = x^2) intersects the x-axis, indicating where (x^2 - x - 2 = 0).

By inspection, we see that the curve intersects the x-axis at approximately (x = -1) and (x = 2).

Therefore, the solutions to the equation (x^2 - x - 2 = 0) are (x = -1) and (x = 2).

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