Mathematical Practices

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Monitoring Progress
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Monitoring Progress 1 Let's start by making an estimate based on the graph. Then, we can check our answer.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.GuessCheckHow to revise -1.5(-1.5)2−1.5−1=-0.25decrease guess -1.6(-1.6)2−1.6−1=-0.04decrease guess -1.61(-1.61)2−1.61−1=-0.0179decrease guess -1.619(-1.619)2−1.619−1=0.002161increase guess -1.618(-1.618)2−1.618−1=-0.000076no change The solution is between -1.618 and -1.619.
Monitoring Progress 2 Let's start by making an estimate based on the graph for the left side of the parabola. Then, we can check our answer.We can identify that when x2+x−3=0, on the left side of the parabola, the point lies somewhere between -2 and -3. We will estimate that x=−2.30 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.GuessCheckHow to revise -2.30(-2.30)2−2.30−3=-0.01decrease guess -2.31(-2.31)2−2.31−3=0.0261increase guess -2.303(-2.303)2−2.303−3=0.000809increase guess -2.302(-2.302)2−2.302−3=-0.002796no change The solution of the left side of the parabola is between -2.303 and -2.302. Let's repeat this process for the right side. We will estimate that x=1.30 Now, let's check our solution.GuessCheckHow to revise 1.301.302+1.30−3=-0.01increase guess 1.311.312+1.31−3=0.0261decrease guess 1.3031.3032+1.303−3=0.000809decrease guess 1.3021.3022+1.302−3=-0.002796no change The solution of the right side of the parabola is between -2.303 and -2.302.