# Quadratic Equations : Formulation of Real-Life Problems and Graphs

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1. Can a graph be used to solve any quadratic equation? Why or why not?

2. Look at the graph below and comment on the sign of D or the discriminant. From the quadratic equation based on the information provided and find its solution.

3. Formulate two word problems from day-to-day life that can be translated to quadratic equations.

4. Based on your readings, list and describe the different methods for solving quadratic equations. Provide examples for each of the methods you listed.

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1. Can a graph be used to solve any quadratic equation? Why or why not?

Yes. Plotting a graph of any quadratic function, if there are no intersections with x-axis, we can conclude that the corresponding quadratic equation has no solution. If there are two intersection points, then we can conclude that the corresponding quadratic equation has two solutions. If there is only one intersection point, then we can conclude that the corresponding quadratic equation has two equal solutions.

2. Look at the graph below and comment on the sign of D or the discriminant. From the quadratic equation based on the information provided and find it solution.

Since there are tow intersection points, we know that this quadratic equation has two real roots. Hence, the sign of D or the discriminant is greater than zero.

Based on the information provided, we know two solutions are x=-1 and x=0.67.

3. Formulate two word problems from day-to-day life that can be translated to quadratic equations.

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#### Solution Summary

Graphs of quadratic equations are investigated and two real-life situations are formulated as quadratic equations. The solution is detailed and well explained.