Question

The graph 4x^2-4x-1 is shown. Use the grpah to find the estimates for the solutions of 4x^2-4x-1=0 and 4x^2 - 4x-1=2

Answer 1

a) The estimates for the solutions of
`4\cdot x^(2)-4\cdot x -1 = 0` are
`x_(1)\approx -0.25` and
`x_(2) \approx 1.25`.

b) The estimates for the solutions of
`4\cdot x^(2)-4\cdot x -1 = 2` are
`x_(1)\approx -0.5` and
`x_(2) \approx 1.5`

Explanation:

From image we get a graphical representation of the second-order polynomial
`y = 4\cdot x^(2)-4\cdot x -1`, where
`x` is related to the horizontal axis of the Cartesian plane, whereas
`y` is related to the vertical axis of this plane. Now we proceed to estimate the solutions for each case:

a)
`4\cdot x^(2)-4\cdot x -1 = 0`

There are two approximate solutions according to the graph, which are marked by red circles in the image attached below:

`x_(1)\approx -0.25`,
`x_(2) \approx 1.25`

b)
`4\cdot x^(2)-4\cdot x -1 = 2`

There are two approximate solutions according to the graph, which are marked by red circles in the image attached below:

`x_(1)\approx -0.5`,
`x_(2) \approx 1.5`