Find the solution of the equation x2 -2x -3 = 0 by graphing.

To solve the equation \(x^2 - 2x - 3 = 0\) by graphing, we need to follow these steps:

1. **Rewrite the equation as a function**:  
   \( y = x^2 - 2x - 3 \)

2. **Graph the function**:  
   Plot the parabola described by the equation \( y = x^2 - 2x - 3 \) on the coordinate plane.

3. **Identify the x-intercepts**:  
   The solutions to the equation \(x^2 - 2x - 3 = 0\) are the x-values where the graph intersects the x-axis (i.e., where \(y = 0\)).

### Steps:

- **Step 1**: Identify key points like the vertex and the axis of symmetry.  
   The axis of symmetry is given by \( x = -\frac{b}{2a} \). Here, \(a = 1\) and \(b = -2\), so:
   \[
   x = \frac{-(-2)}{2(1)} = 1
   \]
   The vertex lies on this line.

- **Step 2**: Compute the vertex by substituting \(x = 1\) into the equation:
   \[
   y = (1)^2 - 2(1) - 3 = 1 - 2 - 3 = -4
   \]
   The vertex is at \( (1, -4) \).

- **Step 3**: Plot additional points to create the shape of the parabola.

- **Step 4**: Draw the graph and identify where it intersects the x-axis.

When you graph the parabola, you will see that it intersects the x-axis at two points, which are the solutions to the equation.

### Graph:
The graph of \( y = x^2 - 2x - 3 \) will intersect the x-axis at \( x = -1 \) and \( x = 3 \).

### Solution:
The solutions to the equation \(x^2 - 2x - 3 = 0\) are \( x = -1 \) and \( x = 3 \).

Would you like more details or have any questions?

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**Related Questions:**

1. How do you find the vertex of a parabola from its equation?
2. How do you solve quadratic equations using the quadratic formula?
3. What is the significance of the discriminant in a quadratic equation?
4. How do you determine the direction of a parabola (whether it opens upwards or downwards)?
5. How do you factor quadratic equations to find their roots?

**Tip:** When graphing a quadratic equation, always start by finding the vertex and axis of symmetry to make plotting easier.

Find the solution of the equation x^2 - 2x - 3 = 0 by graphing.

Discover how to solve the quadratic equation x^2 - 2x - 3 = 0 by graphing. This detailed guide covers key algebraic concepts, including graphing parabolas, identifying x-intercepts, and using the axis of symmetry. Perfect for students in Grades 8-10.

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