The graph of y = 4x2 - 4x – 1 is shown.
Use the graph to find estimates for
the solutions of
i) 4x2 - 4x – 1 = 0
ii) 4x2 - 4x - 1 = 2

Question

Mathematics

Answered

The graph of y = 4x2 - 4x – 1 is shown.
Use the graph to find estimates for
the solutions of
i) 4x2 - 4x – 1 = 0
ii) 4x2 - 4x - 1 = 2

Answer :

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XERO099GO XERO099GO · Answer 1

Answer:

i) The approximate solutions are: [tex]x_{1} \approx -0.207[/tex], [tex]x_{2} \approx 1.207[/tex].

ii) The approximate solutions are: [tex]x_{1}\approx -0.5[/tex], [tex]x_{2} \approx 1.5[/tex].

Step-by-step explanation:

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

[tex]y = 4\cdot x^{2}-4\cdot x - 1[/tex] (1)

[tex]y = 0[/tex] (2)

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

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

[tex]y = 4\cdot x^{2}-4\cdot x - 1[/tex] (1)

[tex]y = 2[/tex] (2)

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