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
1) The solutions are x=5 and x=-1
2) The graph is a parabola opening upwards with its vertex at (2,-9). The x-intercepts are (5,0) and (-1,0) and the y-intercept is (0,-5).
1) To solve the equation x^2 - 4x - 5 = 0, you can use the quadratic formula. The quadratic formula states that for an equation in the form of ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the given equation x^2 - 4x - 5 = 0, we have a = 1, b = -4, and c = -5. Substituting these values into the quadratic formula, we get:
x = (-(-4) ± √((-4)^2 - 4(1)(-5))) / (2(1))
Simplifying further, we have:
x = (4 ± √(16 + 20)) / 2
x = (4 ± √36) / 2
Now, let's calculate the two possible solutions:
x₁ = (4 + √36) / 2 = (4 + 6) / 2 = 10 / 2 = 5
x₂ = (4 - √36) / 2 = (4 - 6) / 2 = -2 / 2 = -1
Therefore, the solutions to the equation x^2 - 4x - 5 = 0 are x = 5 and x = -1.
2) Unfortunately, as an AI text-based bot, I am unable to graphically display the graph of the equation y = x^2 - 4x - 5. However, you can use graphing software or a graphing calculator to plot the graph and visualize it.