Question

The graph of y = 4x2 - 4x – 1 is shown.

Answer 1

Answer:

i) The approximate solutions are: $x_{1} \approx -0.207$, $x_{2} \approx 1.207$.

ii) The approximate solutions are: $x_{1}\approx -0.5$, $x_{2} \approx 1.5$.

Step-by-step explanation:

i) The best approach to estimate graphically the solution of $4\cdot x^{2} - 4\cdot x - 1 = 0$ is graphing the following system of equations:

$y = 4\cdot x^{2}-4\cdot x - 1$ (1)

$y = 0$ (2)

And labeling the points in which both intersects each other. We include the result in the image 'solution-i'. The approximate solutions are: $x_{1} \approx -0.207$, $x_{2} \approx 1.207$.

ii) The best approach to estimate graphically the solution of $4\cdot x^{2} - 4\cdot x - 1 = 2$ is graphing the following system of equations:

$y = 4\cdot x^{2}-4\cdot x - 1$ (1)

$y = 2$ (2)

And labeling the points in which both intersects each other. We include the result in the image 'solution-ii'. The approximate solutions are: $x_{1}\approx -0.5$, $x_{2} \approx 1.5$.