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

.(1 point)
Responses

x=0,1
x equals 0 comma 1

x=2,0
x equals 2 comma 0

no solution
no solution

x=−3,1

Answer 1

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

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

Next, we define a function based on this equation:

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

To find the solutions to the equation \( f(x) = 0 \), we can graph the function \( f(x) \) and look for the x-intercepts, where the graph crosses the x-axis.

Steps to Create the Function Graph:

1. Identify the function: \( f(x) = x^2 + 2x - 3 \)
2. Find the vertex and the x-intercepts.
3. Set the equation to zero and use factoring or the quadratic formula if necessary.

Finding the Roots:

To factor the quadratic equation \( x^2 + 2x - 3 \):

1. We need two numbers that multiply to \(-3\) (the constant term) and add to \(2\) (the coefficient of \(x\)).
2. The numbers \(3\) and \(-1\) satisfy this, so we can factor the equation: \[ (x + 3)(x - 1) = 0 \]

Setting Each Factor to Zero:

1. \( x + 3 = 0 \) gives us \( x = -3 \)
2. \( x - 1 = 0 \) gives us \( x = 1 \)

Summary of Solutions:

The roots of the equation \( x^2 + 2x - 3=0 \) are:

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

Final Answer:

Thus, the solutions are:

x = −3, 1

So the correct response is:

x equals −3 comma 1