Answer:
The ball will land inside the goal.
Explanation:
Given : The flight of the ball is modeled by a parabola.
To find : Will the soccer ball land in the goal?
Solution :
Let the equation of the parabola be,

Where, (h,k) are the vertex of the parabola,
According to question,
A soccer player who is 27 feet from a goal.
Let A be the point where player stand i.e, (27,0)
The height of the goal is 8 feet.
Let B be the point of height of goal i.e, (0,8)
The ball reached a maximum height of 10 feet when it was 15 feet from the soccer player.
The distance from goal to the distance 15 feet away from the player is
27-15=12 feet
Let C be the point with maximum height i.e, (12,10)
C is the vertex of the parabola and A is the point on the parabola.
Then, The equation of parabola is

Point A satisfy the equation,



Substitute back in equation,

Now, we find the y-intercept of the equation i.e, x=0,



If the y-intercept is greater than 8 then the ball will land outside the goal.
If the y-intercept is less than 8 then the ball will land inside the goal.
As 3.6<8
Therefore, The ball will land inside the goal.
Refer the attached figure below.