Mathematics

Question

Use the graph to find estimates for the solutions of
[tex]3x {}^{2} - 3x - 1 = x + 1[/tex]
Use the graph to find estimates for the solutions of [tex]3x {}^{2}  - 3x - 1 = x  + 1[/tex] ​

2 Answer

  • Answer:

    x = - 0.25, x = 1.25

    Step-by-step explanation:

    The solutions to the equation are the values of x where the graph crosses the x- axis, that is as an estimate

    x ≈ - 0.25 and x ≈ 1.25

  • Answer:

    [tex]x=-0.4[/tex]

    [tex]x=1.7[/tex]

    Hopefully the answers are accepted to the nearest tenths.

    Step-by-step explanation:

    Since the left hand side was already graphed, we just need to graph the right hand side which is [tex]x+1[/tex].

    We are going to still let [tex]y[/tex] represent the outputs of [tex]x+1[/tex].

    So we want to graph the equation [tex]y=x+1[/tex] on the same graph as the parabola, the almost U shaped graph.

    You could make a table to plot the equation.

    [tex]y=x+1[/tex]

    [tex]x[/tex]     |      [tex]y[/tex]         |     ordered pair to graph [tex](x,y)[/tex]

    -------------------------------------------------------------------------------------------------------

         -2                     -2+1=-1                          (-2,-1)

         -1                       -1+1=0                           (-1,0)

          0                       0+1=1                            (0,1)

          1                         1+1=2                           (1,2)

          2                        2+1=3                          (2,3)

    The purple line I made is the line formed from these points which was generated from the equation [tex]y=x+1[/tex].

    Now where the blue curve touches the purple line is our solutions. I put those in orange.

    The solutions are approximately, [tex]x=-0.4[/tex] or [tex]x=1.7[/tex].

    Hopefully, it accepts solutions to the nearest tenths.

    We are trying to approximate where those orange dots are on the number line. Please see attachment 2.