Mathematical Practices
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Make an estimate based on the graph. Then, check your answer.
See solution.
We can identify that the negative solution of the parabola lies roughly halfway between -1 and -2. We will estimate that x=-1.5 Now, let's check our solution. We want to increase or decrease our guess based on whether the solution is greater than or less than 0.
| Guess | Check | How to revise |
|---|---|---|
| -1.5 | (-1.5)^2-1.5-1=-0.25 | decrease guess |
| -1.6 | (-1.6)^2-1.6-1=-0.04 | decrease guess |
| -1.61 | (-1.61)^2-1.61-1=-0.0179 | decrease guess |
| -1.619 | (-1.619)^2-1.619-1=0.002161 | increase guess |
| -1.618 | (-1.618)^2-1.618-1=-0.000076 | no change |
The solution is between -1.618 and -1.619.