Find the approximate solution by graphing:

Ask by Beck Nunez. in the United States

Jan 24,2025

Question

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

UpStudy AI · Accepted Answer

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:

$$
\boxed{\,(-3,\ 4)\,}
$$
The approximate solutions are $$ x = -3 $$ and $$ x = 4 $$.

Find the approximate solution by graphing:

Upstudy AI Solution

Answer

Solution

Step 1: Understanding the Equation

Step 2: Solving the Equation Algebraically

Step 3: Comparing with Provided Options

Graphical Interpretation

Conclusion

Bonus Knowledge

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