Solving Word Problems Using Quadratic Equations

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.What is the maximum height the ball reaches, and how far (horizontally) from Audrey does is the ball at its maximum height?

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.What is the maximum height the ball reaches, and how far (horizontally) from Audrey does is the ball at its maximum height?

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Baring errors does mine match your expected result?

Quadratic applications are very helpful in solving several types of word problems (other than the bouquet throwing problem), especially where optimization is involved.

TRACE (CALC), 4 (maximum), moved the cursor to the left of the top after “Left Bound? ” move the cursor anywhere to the right of that zero and hit ENTER. Height versus distance would be the path or trajectory of the bouquet, as in the following problem.

”, moved the cursor to the right of the top after “Right Bound? To get the root, push 2 TRACE (CALC), and then push 2 for ZERO (or move cursor down to ZERO). ” Using the cursors, move the cursor anywhere to the left of the zero (where the graph hits the \(x\)-axis) and hit ENTER. Audrey throws a ball in the air, and the path the ball makes is modeled by the parabola \(y-8=-0.018\), measured in feet.

1/t 1/(t-1min) = 76/360 This leads to 19*t^2 - 180*t 71 = 0 (steps suppressed) The answer is ~9.06 min, the other is less than half a min.

Based on this can you find a discrepancy between your approach and mine?

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

Based on this can you find a discrepancy between your approach and mine?

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.

Again, we can use the vertex to find the maximum or the minimum values, and roots to find solutions to quadratics.

Note that we did a Quadratic Inequality Real World Example here.

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Based on this can you find a discrepancy between your approach and mine? 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.Again, we can use the vertex to find the maximum or the minimum values, and roots to find solutions to quadratics.Note that we did a Quadratic Inequality Real World Example here.Two pedestrians simultaneously head towards each other from two different locations. The first says that by combining their speeds, the two pedestrians cover the 76 km in six hours: $$ = 6\text\cdot60\text.$$ I’m measuring the speeds in km/min, so the time is converted into minutes. How much time does individual pedestrian need in order to walk 1km of path, if the first pedestrians walks this path of 1km one minute less than the other pedestrian? The second one takes $\frac v-1$ minutes to walk $1$ km. We then get $$76=6v 6\cdot \frac $$ Using the formula $t=d/v$, you can write down two equations from the statements in the problem.Student difficulties in solving symbolic problems were mainly associated with arithmetic and algebraic manipulation errors.In the word problems, however, students had difficulties comprehending the context and were therefore unable to formulate the equation to be solved.Thus, it is concluded that the differences in the structural properties of the symbolic equations and word problem representations affected student performance in formulating and solving quadratic equations with one unknown.In this lesson I will teach you about quadratic equation word problems.

$ 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

Based on this can you find a discrepancy between your approach and mine?

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.

Again, we can use the vertex to find the maximum or the minimum values, and roots to find solutions to quadratics.

Note that we did a Quadratic Inequality Real World Example here.

||

Based on this can you find a discrepancy between your approach and mine? 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.Again, we can use the vertex to find the maximum or the minimum values, and roots to find solutions to quadratics.Note that we did a Quadratic Inequality Real World Example here.Two pedestrians simultaneously head towards each other from two different locations. The first says that by combining their speeds, the two pedestrians cover the 76 km in six hours: $$ = 6\text\cdot60\text.$$ I’m measuring the speeds in km/min, so the time is converted into minutes. How much time does individual pedestrian need in order to walk 1km of path, if the first pedestrians walks this path of 1km one minute less than the other pedestrian? The second one takes $\frac v-1$ minutes to walk $1$ km. We then get $$76=6v 6\cdot \frac $$ Using the formula $t=d/v$, you can write down two equations from the statements in the problem.Student difficulties in solving symbolic problems were mainly associated with arithmetic and algebraic manipulation errors.In the word problems, however, students had difficulties comprehending the context and were therefore unable to formulate the equation to be solved.Thus, it is concluded that the differences in the structural properties of the symbolic equations and word problem representations affected student performance in formulating and solving quadratic equations with one unknown.In this lesson I will teach you about quadratic equation word problems.

/v_1$ and

Based on this can you find a discrepancy between your approach and mine?

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.

Again, we can use the vertex to find the maximum or the minimum values, and roots to find solutions to quadratics.

Note that we did a Quadratic Inequality Real World Example here.

||

Based on this can you find a discrepancy between your approach and mine? 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.Again, we can use the vertex to find the maximum or the minimum values, and roots to find solutions to quadratics.Note that we did a Quadratic Inequality Real World Example here.Two pedestrians simultaneously head towards each other from two different locations. The first says that by combining their speeds, the two pedestrians cover the 76 km in six hours: $$ = 6\text\cdot60\text.$$ I’m measuring the speeds in km/min, so the time is converted into minutes. How much time does individual pedestrian need in order to walk 1km of path, if the first pedestrians walks this path of 1km one minute less than the other pedestrian? The second one takes $\frac v-1$ minutes to walk $1$ km. We then get $$76=6v 6\cdot \frac $$ Using the formula $t=d/v$, you can write down two equations from the statements in the problem.Student difficulties in solving symbolic problems were mainly associated with arithmetic and algebraic manipulation errors.In the word problems, however, students had difficulties comprehending the context and were therefore unable to formulate the equation to be solved.Thus, it is concluded that the differences in the structural properties of the symbolic equations and word problem representations affected student performance in formulating and solving quadratic equations with one unknown.In this lesson I will teach you about quadratic equation word problems.

/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.

Again, we can use the vertex to find the maximum or the minimum values, and roots to find solutions to quadratics.

Note that we did a Quadratic Inequality Real World Example here.