Using the vertex of the quadratic equation, it is found that the ball reaches it's maximum height after 2.1 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 equation is given by:
h(t) = -5t² + 21t + 120.
Meaning that the coefficients are a = -5, b = 21, c = 120.
Hence, the time at which the maximum height is reached is given by:
[tex]t_v = -\frac{b}{2a} = -\frac{21}{-10} = 2.1[/tex]
More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967
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