Find the approximate solution by graphing: \( x^{2}-x-12=0 \) \( -3.5,-2.5 \) \( -3,4 \) \( -2.5,4.5 \) \( -4,3 \)

To find the approximate solutions to the quadratic equation \( x^{2} - x - 12 = 0 \) by graphing, let's analyze the given options: 1. **\( (-3.5, -2.5) \)** 2. **\( (-3, 4) \)** 3. **\( (-2.5, 4.5) \)** 4. **\( (-4, 3) \)** ### Step 1: Understanding the Equation The quadratic equation \( x^{2} - x - 12 = 0 \) can be factored or solved using the quadratic formula to find its roots (solutions). ### Step 2: Solving the Equation Algebraically Using the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \( a = 1 \), \( b = -1 \), and \( c = -12 \). \[ x = \frac{1 \pm \sqrt{1 + 48}}{2} = \frac{1 \pm \sqrt{49}}{2} = \frac{1 \pm 7}{2} \] So, the solutions are: \[ x = \frac{1 + 7}{2} = 4 \quad \text{and} \quad x = \frac{1 - 7}{2} = -3 \] ### Step 3: Comparing with Provided Options From the solutions, we have \( x = -3 \) and \( x = 4 \). Looking at the options, the pair **\( (-3, 4) \)** matches our solutions. ### Graphical Interpretation If you graph the equation \( y = x^{2} - x - 12 \), the points where the graph intersects the x-axis are the solutions to the equation. These intersections occur at \( x = -3 \) and \( x = 4 \), confirming our analytical solution. ### **Conclusion** The approximate solutions to the equation \( x^{2} - x - 12 = 0 \) by graphing are: \[ \boxed{\,(-3,\ 4)\,} \]