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=0,1
x equals 0 comma 1

x=2,0
x equals 2 comma 0

x=−3,1
x equals negative 3 comma 1

no solution

Answer 1

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

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

Now we can define a function \(f(x)\):

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

Next, we will find the roots of the function \(f(x)\) where \(f(x) = 0\).

We can start by identifying the graph of the quadratic function \(f(x)\). The graph of a quadratic function is a parabola, and we can find the x-intercepts (the solutions to the equation) by either using factoring, completing the square, or the quadratic formula.

1. **Factoring:**

We want to factor the quadratic expression \(x^2 + 2x - 3\) into the form \((x + p)(x + q) = 0\).

Looking for two numbers that multiply to \(-3\) and add up to \(2\), we find:

\((x + 3)(x - 1) = 0\)

Setting each factor to zero gives:

\[
x + 3 = 0 \implies x = -3
\]
\[
x - 1 = 0 \implies x = 1
\]

So the solutions to the equation \(x^2 + 2x = 3\) (or \(x^2 + 2x - 3 = 0\)) are:

\[
x = -3, \quad x = 1
\]

Now refer to the options provided:

- x=0,1
- x=2,0
- x=−3,1
- no solution

The correct response is:

**x = -3, 1**