Mathematics

Question

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?

2 Answer

  • 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 [tex]y = -0.04x^2 + 1.56x[/tex], 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

    [tex]x=\frac{-b}{2a}[/tex]

    [tex]a=-0.04, b= 1.56[/tex]

    plug in all the values

    [tex]x=\frac{-1.56}{2(-0.04)}=19.5[/tex]

    To find out maximum heigt, plug in 19.5 for x in the given equation

    [tex]y = -0.04x^2 + 1.56x[/tex]

    [tex]-0.04\left(19.5\right)^2\:+\:1.56\left(19.5\right)=15.21[/tex]

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