Question

1) Solve `x^{2}-4x-5=0` and enter solutions below.
2) Push the "Graph It" Button to see a graph of `y=x^{2}-4x-5`
enter solution 1 and 2

Answer 1

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

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

where \(a = 1\), \(b = -4\), and \(c = -5\).

1. Calculate the discriminant:

\[
b^2 - 4ac = (-4)^2 - 4(1)(-5) = 16 + 20 = 36
\]

2. Now apply the quadratic formula:

\[
x = \frac{-(-4) \pm \sqrt{36}}{2(1)} = \frac{4 \pm 6}{2}
\]

3. This gives us two solutions:

\[
x_1 = \frac{4 + 6}{2} = \frac{10}{2} = 5
\]

\[
x_2 = \frac{4 - 6}{2} = \frac{-2}{2} = -1
\]

Thus, the solutions are:

1. Solution 1: \(x = 5\)
2. Solution 2: \(x = -1\)

You can now push the "Graph It" button to visualize the graph of \(y = x^{2} - 4x - 5\).