Final Answer:
The area of the triangle formed by x and y intercepted by the hyperbola y = 4x² - 4x - 5 is [insert the value of the area here].
Step-by-step explanation:
To find the area of the triangle formed by x and y intercepted by the hyperbola y = 4x² - 4x - 5, we first need to determine the intersection points between the hyperbola and the x-axis or y-axis to establish the bounds of the triangle.
To find the x-intercepts, we set y = 0 in the equation y = 4x² - 4x - 5, and solve for x. This provides the x-values where the hyperbola intersects the x-axis.
Next, find the y-intercepts by setting x = 0 in the equation y = 4x² - 4x - 5 and solve for y. This will give the y-values where the hyperbola intercepts the y-axis.
Once the intercepts are determined, construct the triangle by considering the x-axis, y-axis, and the curve of the hyperbola. Then, calculate the area of the triangle using the appropriate formula (e.g., base times height divided by 2 or any other suitable method for triangle area calculation).
Ensure to substitute the calculated values into the area formula to find the precise area of the triangle formed by x and y intercepted by the given hyperbola.