Create a function graph to answer the question. Use the function graph to solve for the solutions to the equation x^2+2x=3

Question

Responses

x=2,0

no solution

x=0,1Create a function graph to answer the question. Use the function graph to solve for the solutions to the equation x^2+2x=3

Responses

x=2,0

no solution

x=0,1

x=−3,1

x=−3,1

Answer 1

To solve the equation \( x^2 + 2x = 3 \) using a function graph, we can follow these steps:

1. Rewrite the equation: \[ x^2 + 2x - 3 = 0 \] This is now in the standard form of a quadratic equation.

2. Define the function: \[ f(x) = x^2 + 2x - 3 \]

3. To find the solutions, we need to find the x-intercepts of the graph of the function \( f(x) \) where \( f(x) = 0 \).

Finding X-Intercepts

1. We'll find the roots of the quadratic equation using factoring or the quadratic formula.
2. The equation factors as: \[ f(x) = (x + 3)(x - 1) \]
3. Setting the factored form to zero: \[ (x + 3)(x - 1) = 0 \]
4. This gives us the solutions:
   • \( x + 3 = 0 \) → \( x = -3 \)
   • \( x - 1 = 0 \) → \( x = 1 \)

Conclusion

The solutions to the equation \( x^2 + 2x = 3 \) are \( x = -3 \) and \( x = 1 \).

Therefore, from the given response options, the correct answer is:

• \( x = -3, 1 \)