9. 1) Solve x2−4x−5=0 and enter solutions below. 2) Push the "Graph It" Button to see a graph of y=x2−4x−5 Enter Solution 1: Enter Solution 2:

Answer 1

To solve the quadratic equation \( x^2 - 4x - 5 = 0 \), we can use the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Here, \( a = 1 \), \( b = -4 \), and \( c = -5 \). Plugging in these values, we get:

\[ x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 \cdot 1 \cdot (-5)}}{2 \cdot 1} \]
\[ x = \frac{4 \pm \sqrt{16 + 20}}{2} \]
\[ x = \frac{4 \pm \sqrt{36}}{2} \]
\[ x = \frac{4 \pm 6}{2} \]

This gives us two solutions:

\[ x = \frac{4 + 6}{2} = \frac{10}{2} = 5 \]
\[ x = \frac{4 - 6}{2} = \frac{-2}{2} = -1 \]

So, the solutions are:

Solution 1: \( x = 5 \)

Solution 2: \( x = -1 \)

If you graph the equation \( y = x^2 - 4x - 5 \), you will see that the parabola intersects the x-axis at \( x = 5 \) and \( x = -1 \).