The solutions of the quadratic equation are estimated as:
x = -0.21
x = 1.21
How to use the graph to find the roots?
The graph of the quadratic equation:
y = 4x² - 4x - 1
is in the image at the end.
We want to use this graph to find the solutions of the equation:
4x² - 4x - 1 = 0
To do so, just identify the values of x at which the parabola intercepts the horizontal axis.
Using the graph, we can see that the two intercepts are at:
x = -0.21
x = 1.21