Question

Use the graph to find estimates for the solutions of


`3x {}^(2) - 3x - 1 = x + 1`
​

Answer 1

x = - 0.25, x = 1.25

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 2

`x=-0.4`

`x=1.7`

Hopefully the answers are accepted to the nearest tenths.

Explanation:

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

We are going to still let
`y` represent the outputs of
`x+1`.

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

You could make a table to plot the equation.

`y=x+1`

`x` |
`y` | ordered pair to graph
`(x,y)`

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

-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
`y=x+1`.

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

The solutions are approximately,
`x=-0.4` or
`x=1.7`.

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.