Respuesta :
The vertex of the quadratic function is of (3,256), which means that a maximum height of 256 feet is obtained after 3 seconds.
What is the vertex of a quadratic equation?
A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
- [tex]x_v = -\frac{b}{2a}[/tex]
- [tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]
Considering the coefficient a, we have that:
- If a < 0, the vertex is a maximum point.
- If a > 0, the vertex is a minimum point.
In this problem, the height of the ball is given by:
f(t) = -16t² + 96t + 112.
Hence the coefficients are a = -16 < 0, b = 96, c = 112, and the coordinates of the vertex are:
- [tex]x_v = -\frac{96}{2(-16)} = 3[/tex]
- [tex]y_v = -\frac{96^2 - 4(-16)(112)}{4(-16)} = 256[/tex]
The vertex of the quadratic function is of (3,256), which means that a maximum height of 256 feet is obtained after 3 seconds.
More can be learned about the vertex of a quadratic function at https://brainly.com/question/24737967
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