Question

Create a function graph to answer the question. Use the function graph to solve for the solutions to the equation x2+2x=3
.(1 point)
Responses

x=−3,1
x equals negative 3 comma 1

no solution
no solution

x=2,0
x equals 2 comma 0

x=0,1

Answer 1

To solve the equation \( x^2 + 2x = 3 \) using the function graph method, we can first rewrite the equation in standard form:

\[
x^2 + 2x - 3 = 0
\]

Now, we can define a function \( f(x) \) based on the left side of the equation:

\[
f(x) = x^2 + 2x - 3
\]

To find the solutions to the equation, we need to determine where the graph of \( f(x) \) intersects the x-axis, which occurs when \( f(x) = 0 \).

### Steps:

1. **Finding the Roots**: We can use the quadratic formula to find the roots of the equation:

\[
x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}
\]

In our case:
- \( a = 1 \)
- \( b = 2 \)
- \( c = -3 \)

Calculating the discriminant:

\[
b^2 - 4ac = 2^2 - 4(1)(-3) = 4 + 12 = 16
\]

Now, substituting the values into the quadratic formula:

\[
x = \frac{{-2 \pm \sqrt{16}}}{2 \cdot 1} = \frac{{-2 \pm 4}}{2}
\]

Calculating the potential solutions:

1. \( x = \frac{{-2 + 4}}{2} = \frac{2}{2} = 1 \)
2. \( x = \frac{{-2 - 4}}{2} = \frac{{-6}}{2} = -3 \)

### Solutions:

The solutions to the equation \( x^2 + 2x = 3 \) are:

\[
x = -3 \quad \text{and} \quad x = 1
\]

### Conclusion:

The options provided included:

- \( x = -3, 1 \)
- no solution
- \( x = 2, 0 \)
- \( x = 0, 1 \)

The correct response is:

**x = -3, 1**