what is the soltion of these to problems
A. x^2 - 4x - 5 = 0
B. y = x^2 - 4x - 5
To find the solution for problem A:
x^2 - 4x - 5 = 0
This is a quadratic equation, so we can use the quadratic formula to find the solution:
x = (-b ± √(b^2 - 4ac)) / 2a
Here, a = 1, b = -4, and c = -5.
Plugging these values into the formula:
x = (4 ± √(16 + 20)) / 2
x = (4 ± √36) / 2
x = (4 ± 6) / 2
Solving for both cases:
x = (4 + 6) / 2 = 5
x = (4 - 6) / 2 = -1
Therefore, the solutions for problem A are x = 5 and x = -1.
For problem B:
y = x^2 - 4x - 5
This is an equation of a function. The solution is actually a parabola, which we can graph to visualize. The parabola is a shape that opens upwards with a vertex at the minimum point (-b, a - (b^2 / 4a)).
For the equation y = x^2 - 4x - 5, the vertex will be at x = 2, y = -9 (a = 1, b = -4).
Note: The parabola opens upwards, so the y values will be minimized at this vertex and the shape will be a curve symmetric about this point.