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Sagot :
Answer:
a) The ball reaches it's maximum height after 3 seconds.
b) The maximum height of the ball is of 151 feet.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
In this question:
The height of the ball is modeled by:
[tex]h(t) = -16t^2 + 96t + 7[/tex]
So a quadratic equation with [tex]a = -16, b = 96, c = 7[/tex]
a) After how many seconds will the ball reach its maximum height?
t-value of the vertex. So
[tex]t_{v} = -\frac{96}{2(-16)} = 3[/tex]
The ball reaches it's maximum height after 3 seconds.
b) What is that maximum height?
h of the vertex.
[tex]\Delta = b^2 - 4ac = (96)^2 - 4(-16)(7) = 9664[/tex]
[tex]h_{v} = -\frac{9664}{4(-16)} = 604[/tex]
The maximum height of the ball is of 151 feet.
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