Height and Distance If an object is projected from the ground and lands on the ground some distance away, it follows a parabolic trajectory that may be graphed in the first quadrant of a Cartesian plane. When the trajectory is represented in this way, its equation may be written in the following form: y = ax² + bx, where a <0 and b>0. Consider the height h of the object's trajectory and the distance d it travels. In the graph above, as you can see, the height is greater than the distance travelled. However, this is not always the case. The height may be less than or equal to the distance; this depends on the equation. ▶Determine what the values of parameters a and b have to be for the height of the trajectory to be greater than the distance travelled. Explain your reasoning by justifying each step in your calculations.
Height and Distance If an object is projected from the ground and lands on the ground some distance away, it follows a parabolic trajectory that may be graphed in the first quadrant of a Cartesian plane. When the trajectory is represented in this way, its equation may be written in the following form: y = ax² + bx, where a <0 and b>0. Consider the height h of the object's trajectory and the distance d it travels. In the graph above, as you can see, the height is greater than the distance travelled. However, this is not always the case. The height may be less than or equal to the distance; this depends on the equation. ▶Determine what the values of parameters a and b have to be for the height of the trajectory to be greater than the distance travelled. Explain your reasoning by justifying each step in your calculations.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.7: Solving Systems Of Linear And Quadratic Equations
Problem 21PPS
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Transcribed Image Text:Height and Distance
If an object is projected from the ground and lands on the ground some distance away, it follows a parabolic
trajectory that may be graphed in the first quadrant of a Cartesian plane. When the trajectory is represented
in this way, its equation may be written in the following form: y = ax² + bx, where a <0 and b>0.
Consider the height h of the object's trajectory and the distance d it travels. In the graph above, as you can
see, the height is greater than the distance travelled. However, this is not always the case. The height may
be less than or equal to the distance; this depends on the equation.
Determine what the values of parameters a and b have to be for the height of the trajectory
to be greater than the distance travelled. Explain your reasoning by justifying each step in
your calculations.
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