Solving Word Problems Using Quadratic Equations

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The amount of effort you invest in practicing solving word problems will be directional proportional to your mastery of them.

Lastly, quadratic equation word problems are interesting and I think fun- really study hard as these type of problems are on many tests to include the SAT/ACT.

Note also that we will discuss Optimization Problems using Calculus in the Optimization section here.

where \(t\) is the time in seconds, and \(h\) is the height of the ball.

Solution: Note that in this problem, the \(x\)-axis is measuring the horizontal distance of the path of the ball, not the time, so when we draw the parabola, it’s a true indication of the trajectory or path of the ball.

Note also that the equation given is in vertex form (if we add Since the quadratic is already in vertex form (\(y=a k\), where \((h,k)\) is the vertex), we can see that the vertex from \(0=-0.018 8\) is \((20,8)\).

If the first one walks $v$ km/hour, he takes $\frac v$ minutes to walk

Note also that the equation given is in vertex form (if we add Since the quadratic is already in vertex form (\(y=a k\), where \((h,k)\) is the vertex), we can see that the vertex from \(0=-0.018 8\) is \((20,8)\).

If the first one walks $v$ km/hour, he takes $\frac v$ minutes to walk $1$ km.

The second fact is that it takes the second pedestrian one more minute than the first to cover 1 km, so you have $$\frac1 1=\frac1.$$ Solve the two equations for $v_1$ and $v_2$ and then compute $1/v_1$ and $1/v_2=1/v_1 1$, or substitute $t_1=1/v_1$ and $t_2=1/v_2$ into the two equations and solve for the times directly.

Find the highest point that her golf ball reached and also when it hits the ground again.

Find a reasonable domain and range for this situation.

||

Note also that the equation given is in vertex form (if we add Since the quadratic is already in vertex form (\(y=a k\), where \((h,k)\) is the vertex), we can see that the vertex from \(0=-0.018 8\) is \((20,8)\). If the first one walks $v$ km/hour, he takes $\frac v$ minutes to walk $1$ km.The second fact is that it takes the second pedestrian one more minute than the first to cover 1 km, so you have $$\frac1 1=\frac1.$$ Solve the two equations for $v_1$ and $v_2$ and then compute $1/v_1$ and $1/v_2=1/v_1 1$, or substitute $t_1=1/v_1$ and $t_2=1/v_2$ into the two equations and solve for the times directly.Find the highest point that her golf ball reached and also when it hits the ground again.Find a reasonable domain and range for this situation.In addition, the students’ written responses and interview data were qualitatively analyzed to determine the nature of the students’ difficulties in formulating and solving quadratic equations.The findings revealed that although students have difficulties in solving both symbolic quadratic equations and quadratic word problems, they performed better in the context of symbolic equations compared with word problems.Data was collected through an open-ended questionnaire comprising eight symbolic equations and four word problems; furthermore, semi-structured interviews were conducted with sixteen of the students.In the data analysis, the percentage of the students’ correct, incorrect, blank, and incomplete responses was determined to obtain an overview of student performance in solving symbolic equations and word problems.What is the maximum height the ball reaches, and how far (horizontally) from Audrey does is the ball at its maximum height?How far does the ball travel before it hits the ground?

$ km.

The second fact is that it takes the second pedestrian one more minute than the first to cover 1 km, so you have $$\frac1 1=\frac1.$$ Solve the two equations for $v_1$ and $v_2$ and then compute

Note also that the equation given is in vertex form (if we add Since the quadratic is already in vertex form (\(y=a k\), where \((h,k)\) is the vertex), we can see that the vertex from \(0=-0.018 8\) is \((20,8)\).

If the first one walks $v$ km/hour, he takes $\frac v$ minutes to walk $1$ km.

The second fact is that it takes the second pedestrian one more minute than the first to cover 1 km, so you have $$\frac1 1=\frac1.$$ Solve the two equations for $v_1$ and $v_2$ and then compute $1/v_1$ and $1/v_2=1/v_1 1$, or substitute $t_1=1/v_1$ and $t_2=1/v_2$ into the two equations and solve for the times directly.

Find the highest point that her golf ball reached and also when it hits the ground again.

Find a reasonable domain and range for this situation.

||

Note also that the equation given is in vertex form (if we add Since the quadratic is already in vertex form (\(y=a k\), where \((h,k)\) is the vertex), we can see that the vertex from \(0=-0.018 8\) is \((20,8)\). If the first one walks $v$ km/hour, he takes $\frac v$ minutes to walk $1$ km.The second fact is that it takes the second pedestrian one more minute than the first to cover 1 km, so you have $$\frac1 1=\frac1.$$ Solve the two equations for $v_1$ and $v_2$ and then compute $1/v_1$ and $1/v_2=1/v_1 1$, or substitute $t_1=1/v_1$ and $t_2=1/v_2$ into the two equations and solve for the times directly.Find the highest point that her golf ball reached and also when it hits the ground again.Find a reasonable domain and range for this situation.In addition, the students’ written responses and interview data were qualitatively analyzed to determine the nature of the students’ difficulties in formulating and solving quadratic equations.The findings revealed that although students have difficulties in solving both symbolic quadratic equations and quadratic word problems, they performed better in the context of symbolic equations compared with word problems.Data was collected through an open-ended questionnaire comprising eight symbolic equations and four word problems; furthermore, semi-structured interviews were conducted with sixteen of the students.In the data analysis, the percentage of the students’ correct, incorrect, blank, and incomplete responses was determined to obtain an overview of student performance in solving symbolic equations and word problems.What is the maximum height the ball reaches, and how far (horizontally) from Audrey does is the ball at its maximum height?How far does the ball travel before it hits the ground?

/v_1$ and

Note also that the equation given is in vertex form (if we add Since the quadratic is already in vertex form (\(y=a k\), where \((h,k)\) is the vertex), we can see that the vertex from \(0=-0.018 8\) is \((20,8)\).

If the first one walks $v$ km/hour, he takes $\frac v$ minutes to walk $1$ km.

The second fact is that it takes the second pedestrian one more minute than the first to cover 1 km, so you have $$\frac1 1=\frac1.$$ Solve the two equations for $v_1$ and $v_2$ and then compute $1/v_1$ and $1/v_2=1/v_1 1$, or substitute $t_1=1/v_1$ and $t_2=1/v_2$ into the two equations and solve for the times directly.

Find the highest point that her golf ball reached and also when it hits the ground again.

Find a reasonable domain and range for this situation.

||

Note also that the equation given is in vertex form (if we add Since the quadratic is already in vertex form (\(y=a k\), where \((h,k)\) is the vertex), we can see that the vertex from \(0=-0.018 8\) is \((20,8)\). If the first one walks $v$ km/hour, he takes $\frac v$ minutes to walk $1$ km.The second fact is that it takes the second pedestrian one more minute than the first to cover 1 km, so you have $$\frac1 1=\frac1.$$ Solve the two equations for $v_1$ and $v_2$ and then compute $1/v_1$ and $1/v_2=1/v_1 1$, or substitute $t_1=1/v_1$ and $t_2=1/v_2$ into the two equations and solve for the times directly.Find the highest point that her golf ball reached and also when it hits the ground again.Find a reasonable domain and range for this situation.In addition, the students’ written responses and interview data were qualitatively analyzed to determine the nature of the students’ difficulties in formulating and solving quadratic equations.The findings revealed that although students have difficulties in solving both symbolic quadratic equations and quadratic word problems, they performed better in the context of symbolic equations compared with word problems.Data was collected through an open-ended questionnaire comprising eight symbolic equations and four word problems; furthermore, semi-structured interviews were conducted with sixteen of the students.In the data analysis, the percentage of the students’ correct, incorrect, blank, and incomplete responses was determined to obtain an overview of student performance in solving symbolic equations and word problems.What is the maximum height the ball reaches, and how far (horizontally) from Audrey does is the ball at its maximum height?How far does the ball travel before it hits the ground?

/v_2=1/v_1 1$, or substitute $t_1=1/v_1$ and $t_2=1/v_2$ into the two equations and solve for the times directly.

Find the highest point that her golf ball reached and also when it hits the ground again.

Find a reasonable domain and range for this situation.

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