Question

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

x=2,0
𝑥
=
2
,
0
x equals 2 comma 0

x=0,1
𝑥
=
0
,
1
x equals 0 comma 1

no solution
no solution

x=−3,1

Answer 1

To solve the equation \( x^2 + 2x = 3 \) using a function graph, we can rearrange the equation to form a standard quadratic equation:

1. Subtract 3 from both sides:
\[
x^2 + 2x - 3 = 0
\]

Now we can reference the function \( f(x) = x^2 + 2x - 3 \).

### Steps to graph \( f(x) \):

1. **Determine the vertex**: The vertex form for a quadratic is given by \( x = -\frac{b}{2a} \).
- Here, \( a = 1 \) and \( b = 2 \).
- So the vertex \( x \) coordinate is \( x = -\frac{2}{2(1)} = -1 \).
- Substituting \( x = -1 \) into the equation to find the \( y \) coordinate:
\[
f(-1) = (-1)^2 + 2(-1) - 3 = 1 - 2 - 3 = -4.
\]
- Thus, the vertex is at \( (-1, -4) \).

2. **Find the x-intercepts**: Set \( f(x) = 0 \).
\[
x^2 + 2x - 3 = 0.
\]
- This can be factored:
\[
(x + 3)(x - 1) = 0.
\]
- The solutions are:
\[
x + 3 = 0 \rightarrow x = -3,
\]
\[
x - 1 = 0 \rightarrow x = 1.
\]

3. **Graph the function**:
- The parabola opens upwards (since \( a > 0 \)).
- The x-intercepts are at \( x = -3 \) and \( x = 1 \).
- The vertex is at \( (-1, -4) \), which is below the x-axis.

### Conclusion:
From the graph or the factored form, we can conclude that the solutions to the equation \( x^2 + 2x - 3 = 0 \) are:

\[
\boxed{x = -3, 1}
\]

So, the correct response is:

**x = −3, 1**.