Respuesta :
After 8 seconds the ball height was 42 units.
It is given that on a game show, contestants shoot a foam ball toward a target. The table includes points along one path the ball can take to hit the target where x is the time that has passed since the ball was launched and y is the height at this time.
It is required to find how high was the ball after 8 seconds.
What is a parabola?
It is defined as the graph of a quadratic function that has something bowl-shaped.
The orbit of the ball will be a parabola.
We know the standard form of a quadratic function:
[tex]\rm y=ax^2+bx+c[/tex] where [tex]\rm \\a\neq 0[/tex]
At x = 0 and y = 10, we get:
[tex]\rm 10 =a(0)^2+b(0)+c\\\rm 10= c\\\rm c=10[/tex]
At x = 2 and y=24, we get:
[tex]\rm 24= a(2)^2+b(2)+c\\\rm 24=4a+2b+10\\\rm 4a+2b=14[/tex]....(1)
At x = 16 and y = 10, we get:
[tex]\rm 10= a(16)^2+b(16)+c\\\rm 10=256a+16b+10\\\rm 256a+16b=0 \\[/tex]....(2)
By solving equations (1) and (2), we get;
a = - 1/2, b = 8 and c = 10
Putting these values in the standard form of a quadratic function, we get:
[tex]\rm y = - \frac{1}{2} x^2+8x+10\\[/tex]
Now, after 8 seconds means when x = 8, we get:
[tex]\rm y=-\frac{1}{2}\times 8^2 +8\times8+10\\\rm y = -32+64+10\\\rm y= 42[/tex]
Thus, after 8 seconds the ball height was 42 units.
Know more about the parabola here:
https://brainly.com/question/8708520
