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

Question

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.