1. Solve the quadratic equation by graphing it. Select all possible answers.
\[
\begin{array}{l}
-x^{2}-4 x=3 \\
x=?
\end{array}
\]
$-0.5$
$-1$
$-3$
3
0.5
1
No real solutions
Answer
\(\boxed{-3, -1}\)
Step 1 ：Rewrite the equation in the standard form of a quadratic equation: \(ax^2 + bx + c = 0\)
Step 2 ：\(-x^2 - 4x = 3\) becomes \(x^2 + 4x + 3 = 0\)
Step 3 ：Find the discriminant: \(D = b^2 - 4ac\)
Step 4 ：\(D = (-4)^2 - 4(1)(3) = 16 - 12 = 4\)
Step 5 ：Since the discriminant is positive, there are two real solutions. Use the quadratic formula to find the solutions: \(x = \frac{-b \pm \sqrt{D}}{2a}\)
Step 6 ：\(x_1 = \frac{-(-4) + \sqrt{4}}{2(1)} = \frac{4 + 2}{2} = \frac{6}{2} = 3\)
Step 7 ：\(x_2 = \frac{-(-4) - \sqrt{4}}{2(1)} = \frac{4 - 2}{2} = \frac{2}{2} = 1\)
Step 8 ：\(\boxed{-3, -1}\)
