Using quadratic function concepts, it is found that:
The height of the pumpkin after x seconds is modeled by:
[tex]y = -16x^2 + 95x + 10[/tex]
Which is a quadratic equation with coefficients [tex]a = -16, b = 95, c = 10[/tex].
The maximum height is the y-value of the vertex, given by:
[tex]y_{MAX} = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}[/tex]
Hence:
[tex]\Delta = b^2 - 4ac = (95)^2 - 4(-16)(10) = 9665[/tex]
[tex]y_{MAX} = -\frac{\Delta}{4a} = -\frac{9665}{4(-16)} = 151[/tex]
The maximum height of the pumpkin is of 151 feet.
It hits the ground when [tex]y = 0[/tex], hence:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{-95 + \sqrt{9665}}{2(-16)} = -0.1[/tex]
[tex]x_2 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{-95 - \sqrt{9665}}{2(-16)} = 6.04[/tex]
The pumpkin hits the ground after 6.04 seconds.
To learn more about quadratic functions, you can check https://brainly.com/question/24737967
