The path of a football kicked by a field goal kicker can be modeled by the equation y = –0.04x2 + 1.56x, where x is the horizontal distance in yards and y is the corresponding height in yards. What is the approximate maximum height of the football?
convert to vertex form:-
= -0.04(x^2 + 39x)
= -0.04( (x + 19.5)^2 - 380.25)
vertex is at -0.04 * -380.25 = 15.21 yards
Maximum height is about 15.2 yards
Answer:
Maximum height is 15.21 yards
Step-by-step explanation:
The path of a football kicked by a field goal kicker can be modeled by the equation \(y = -0.04x^2 + 1.56x\), where x is the horizontal distance in yards and y is the corresponding height in yards
MAximum height occurs at the vertex
Lets find x coordinate of vertex using formula
\(x=\frac{-b}{2a}\)
\(a=-0.04, b= 1.56\)
plug in all the values
\(x=\frac{-1.56}{2(-0.04)}=19.5\)
To find out maximum heigt, plug in 19.5 for x in the given equation
\(y = -0.04x^2 + 1.56x\)
\(-0.04\left(19.5\right)^2\:+\:1.56\left(19.5\right)=15.21\)