Larry likes skeet shooting, where a clay disc is shot into the air, and the participant tries to shoot it as it flies through the air. The discs are released from a ring mechanism that sits at ground level and shoots the disc on average a horizontal distance of 120 m on a parabolic path. On average, the skeet hits a height of 37.5 m after travelling a horizontal distance of 45 m.
a.) Sketch and label a diagram that represents the given information
b.) Determine the equation of a function, in standard form, that represents the flight of the clay disc. Leave values as fractions.
c.) Determine the average maximum height of the skeet by completing the square.
PART A
Your diagram should be an upside-down parabola, with one zero at x = 0 and another at x = 120 (the maximum distance the skeet flies). It should also pass through the point (45, 37.5) and the peak should occur at x = 60 (unknown y at the moment)
PART B
y = k(x – p)(x – q), where p and q are the zeros, so this equation turns into
y = k(x-120)(x)
y = k(x2 - 120x)
To solve for k, we plug in our known point (45, 37.5)
37.5 = k(452 - 120*45)
k = -1/90
PART C
We now have our equation
y = -1/90(x2 - 120x)
==> distribute the -1/90 into the fraction
y = -x2/90 + 4x/3
==> Maybe we should first multiply both sides by –90, to make factoring right side easier.
–90y = x2 – (360/3)x
–90y = x2 – 120x
==> Take half of –120 and square it: (–60)2 = 3600. Add to both sides.
–90y + 3600 = x2 – 120x + 3600
==> Factor right side as a perfect square.
–90y + 3600 = (x – 60)(x – 60)
==> Divide both sides by –90.
y = (–1/90)*(x – 60)2 + 40
That form is called vertex form. The vertex is (60, 40), which is the maximum y value the function will obtain!
3 years ago
Answered By Emily D
Hey I think you're missing most of this question!
Larry likes skeet shooting, where a clay disc is shot into the air, and the participant tries to shoot it as it flies through the air. The discs are released from a ring mechanism that sits at ground level and shoots the disc on average a horizontal distance of 120 m on a parabolic path. On average, the skeet hits a height of 37.5 m after travelling a horizontal distance of 45 m.
a.) Sketch and label a diagram that represents the given information
b.) Determine the equation of a function, in standard form, that represents the flight of the clay disc. Leave values as fractions.
c.) Determine the average maximum height of the skeet by completing the square.
PART A
Your diagram should be an upside-down parabola, with one zero at x = 0 and another at x = 120 (the maximum distance the skeet flies). It should also pass through the point (45, 37.5) and the peak should occur at x = 60 (unknown y at the moment)
PART B
y = k(x – p)(x – q), where p and q are the zeros, so this equation turns into
y = k(x-120)(x)
y = k(x2 - 120x)
To solve for k, we plug in our known point (45, 37.5)
37.5 = k(452 - 120*45)
k = -1/90
PART C
We now have our equation
y = -1/90(x2 - 120x)
==> distribute the -1/90 into the fraction
y = -x2/90 + 4x/3
==> Maybe we should first multiply both sides by –90, to make factoring right side easier.
–90y = x2 – (360/3)x
–90y = x2 – 120x
==> Take half of –120 and square it: (–60)2 = 3600. Add to both sides.
–90y + 3600 = x2 – 120x + 3600
==> Factor right side as a perfect square.
–90y + 3600 = (x – 60)(x – 60)
==> Divide both sides by –90.
y = (–1/90)*(x – 60)2 + 40
That form is called vertex form. The vertex is (60, 40), which is the maximum y value the function will obtain!