Question

A bottle rocket that was made in science class had a trajectory path that followed the quadratic equation y=-x^2+4x+6. What is the turning point of the rocket's path?

1) (1,5)
2) (2,10)
3) (-2,-10)
4) (1,-5)

Answer 1

`y=-x^2+4x+6 \\ \\a =-1, \ b = 4 , \ c=6 \\ \\ The \ vertex \ is \ (x,f(x)) \\ \\x=(-b)/(2a) =(-4)/(2\cdot (-1))=(-4)/(-2)=2\\ \\ f(2)=-x^2+4x+6 =-2^2+4 \cdot 2+6 =-4+8+6=10 \\ \\ The \ vertex \ is \ (2,10) \\ \\ \\ Answer: \ 2) \ \ (2,10)`