To represent the scenario of Lorraine hitting the golf ball, we can formulate it as a quadratic equation.
-
Equation: The ball's flight can be modeled by a quadratic equation in the form
, where represents the height of the ball and represents the horizontal distance from Lorraine. -
Landing Point: The ball lands 60 feet away from her, which means this point can be represented as
. This is the x-intercept of the parabola. -
Axis of Symmetry: The axis of symmetry for a parabola described by a quadratic equation is located at the vertex and can be found at
, where and are the x-intercept points. Since the ball lands 60 feet away and starts at 0 feet away, the distance from the launch point to the landing point is 60 feet. Thus, the halfway point for the axis of symmetry is located at: -
Vertex: Given that the highest point of the ball's trajectory is 30 feet in the air, the vertex of the parabola is at
. -
Starting Point: The ball starts at 0 feet away from Lorraine, so another point on the graph would be
. -
Missing Value: Using the information given, the only value that is not explicitly stated and needs to be found is the coefficient
in the quadratic equation. This coefficient determines how "wide" or "narrow" the parabola is.
To summarize:
- The scenario is best represented by a quadratic equation.
- The ball lands 60 feet away represents the
-intercept. - Half of this distance gives the axis of symmetry at 30 feet.
- The vertex is at
. - The ball starts at
. - The missing value to be determined is the coefficient
.