Parametric Equation Problem A mellophone player is marching from the Side 1 End Zone at (-15,-6) to the point (7,5), 3 steps outside the 30 Yard Line on Side 2 along the path:

When written in a parametric form it is:

When will he or she arrive at the end spot?
This problem can be done two ways, using the x-value and using the y-value. For this question, I will use x.

88 Steps How big of steps did the mellophone player take?

So use the Pythagorean Theorem.

On what beat will he or she cross the 50 Yard Line? (y-axis)
For this question, begin by making x zero.

60 Steps Unfortunately, the band director arranged another band member that intercepts with this mellophone's path. The other band member walks along the path y=-2x+5. Where do they intersect?
Start by taking both points and setting them equal to one another.

Now enter the x-value back into the original problem.

(1.16667,2.08333) When do they intersect?
For this question, I will use the x-value.

65.6667 Steps Where is he or she on step 85?
Begin by entering 85 in for t in both parts of the equation

(-5,-1) On what step will he or she be in line with the field goals? (the x-axis)
Solve this one the same way as above, only make y equal zero.

48 Steps If at a band competition, stepping off the field in the show would cause a penalty. On what step would he or she step off the field? (stepping on the point (13,8))
Just like the first problem, you can use either the x or the y value for this one, but for this example, I will use y.

112 Steps While marching, the mellophone will pass h;is or her friend's end point. It is at the point and (-2,2). When is the mellophone closest to him or her?
To do this, use the distance formula and graph it

When plugged into the calculator, the x-value of the minimum is -3.2. Now to use it to find the y-value:

When written in a parametric form it is:

When will he or she arrive at the end spot?This problem can be done two ways, using the x-value and using the y-value. For this question, I will use x.

88 Steps

How big of steps did the mellophone player take?So use the Pythagorean Theorem.

On what beat will he or she cross the 50 Yard Line? (y-axis)For this question, begin by making x zero.

60 Steps

Unfortunately, the band director arranged another band member that intercepts with this mellophone's path. The other band member walks along the path y=-2x+5. Where do they intersect?Start by taking both points and setting them equal to one another.

Now enter the x-value back into the original problem.

(1.16667,2.08333)

When do they intersect?For this question, I will use the x-value.

65.6667 Steps

Where is he or she on step 85?Begin by entering 85 in for t in both parts of the equation

(-5,-1)

On what step will he or she be in line with the field goals? (the x-axis)Solve this one the same way as above, only make y equal zero.

48 Steps

If at a band competition, stepping off the field in the show would cause a penalty. On what step would he or she step off the field? (stepping on the point (13,8))Just like the first problem, you can use either the x or the y value for this one, but for this example, I will use y.

112 Steps

While marching, the mellophone will pass h;is or her friend's end point. It is at the point and (-2,2). When is the mellophone closest to him or her?To do this, use the distance formula and graph it

When plugged into the calculator, the x-value of the minimum is -3.2. Now to use it to find the y-value:

The closest point is at the point (-3.2,-0.1)

Example of what it looks like:

Note for the applet: 1 beat = 1 step