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Lorraine hits a golf ball into the air. It lands 60 feet away from her. At its highest point, the ball is 30 feet in the air.

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(6 points)
This scenario would best be represented by a
blank equation.

The ball lands 60 feet away from her would represent the
blank Half of this distance would be axis of symmetry. That would make the vertex blank

The ball starts at how many feet away from Lorraine?
blank So another point on the graph would be blank

1 answer

Let's break down the information given to fill in the blanks and understand the scenario better:

  1. Form of the Equation: Since the motion of the golf ball can be modeled as a projectile, it typically follows a parabolic path. The equation can be expressed in the form of a quadratic function \(y = a(x - h)^2 + k\) where \((h, k)\) is the vertex of the parabola.

  2. Distance and Height:

    • The ball lands 60 feet away from Lorraine, which represents the horizontal distance (or \(x\)-coordinate when considering the trajectory of the ball).
    • The highest point (30 feet) of the ball's trajectory is the maximum height, which corresponds to the \(y\)-coordinate of the vertex.

  3. Axis of Symmetry:

    • The axis of symmetry is a vertical line that passes through the vertex of the parabola. Since the ball lands 60 feet away from Lorraine, the axis of symmetry would be half of this distance: \( \frac{60}{2} = 30 \) feet from Lorraine.
    • Therefore, the axis of symmetry is at \(x = 30\) feet.

  4. Vertex:

    • The vertex of the parabola occurs at the highest point, which we've established to be at \((30, 30)\).

  5. Initial Position:

    • The ball starts at Lorraine's position, which is 0 feet from her. So the starting position has coordinates \((0, 0)\).

  6. Points on the Graph:

    • The point where the ball lands is \((60, 0)\).

Putting all of that together, we can fill in the blanks:

  • This scenario would best be represented by a quadratic equation.
  • The ball lands 60 feet away from her would represent the width of the parabolic path. Half of this distance would be 30 (the axis of symmetry). That would make the vertex (30, 30).
  • The ball starts at how many feet away from Lorraine? 0 feet. So another point on the graph would be (60, 0).

Here are the filled-in answers:

  1. This scenario would best be represented by a quadratic equation.
  2. The ball lands 60 feet away from her would represent the width of the parabolic path. Half of this distance would be 30 (the axis of symmetry). That would make the vertex (30, 30).
  3. The ball starts at how many feet away from Lorraine? 0 feet. So another point on the graph would be (60, 0).