Answer:
(1) - Upside-down parabola
(2) - x=0 and x=150
(3) - A negative, "-"
(4) - y=-1/375(x–75)²+15
(5) - y≈8.33 yards
Explanation:
(1) - What shape does the flight of the ball take?
The flight path of the ball forms the shape of an upside-down parabola.
(2) - What are the zeros (x-intercepts) of the function?
The zeros (also known as x-intercepts or roots) of a function are the points where the graph of the function intersects the x-axis. At these points, the value of the function is zero.
Thus, we can conclude that the zeros of the given function are 0 and 150.
(3) - What would be the sign of the leading coefficient "a?"
In a quadratic function of the form f(x) = ax²+bx+c, the coefficient "a" determines the orientation of the parabola.
- If "a" is positive, the parabola opens upward. This is because as x moves further away from the vertex of the parabola, the value of the function increases.
- If "a" is negative, the parabola opens downward. This is because as x moves further away from the vertex, the value of the function decreases.
Therefore, the sign would be "-" (negative), as this would open the parabola downwards.
(4) - Write the function
Using the following form of a parabola to determine the proper function,
y=a(x–h)²+k
Where:
- (h,k) is the vertex of the parabola
- a is the leading coefficient we can find using another point
We know "a" has to be negative so,
=> y=-a(x–h)²+k
The vertex of the given parabola is (75,15). Plugging this in we get,
=> y=-a( x–75)²+15
Use the point (0,0) to find the value of a.
=> y=-a(x–75)²+15
=> 0=-a(0–75)²+15
=> 0=-a(–75)²+15
=> 0=-5625a+15
=> -15=-5625a
∴ a=1/375
Thus, the equation of the given parabola is written as...
y=-1/375(x–75)²+15
(5) - What is the height of the ball when it has traveled horizontally 125 yards?
Substitute in x=125 and solve for y.
y=-1/375(x–75)²+15
=> y=-1/375(125–75)²+15
=> y=-1/375(50)²+15
=> y=-2500/375+15
=> y=-20/3+15
=> y=25/3
∴ y≈8.33 yards