Answer:
93.5 units
Explanation:
The function that models the approximate height is given as:
[tex]f\mleft(t\mright)=-6t^2+42t+20[/tex]To determine how high the object goes, we find the maximum height ( or vertex) of the parabola.
First, find the equation of the line of symmetry using the formula below:
[tex]x=-\frac{b}{2a}[/tex][tex]\begin{gathered} a=-6,b=42 \\ \implies t=\frac{-42}{2(-6)} \\ =\frac{42}{12} \\ t=3.5 \end{gathered}[/tex]Next, substitute t=3.5 into f(t) to find the maximum height.
[tex]\begin{gathered} f\mleft(t\mright)=-6t^2+42t+20 \\ f(3.5)=-6(3.5)^2+42(3.5)+20 \\ =93.5 \end{gathered}[/tex]The object goes as high as 93.5 units.
To demonstrate, the graph is attached here:
We see that the graph goes as high as 93.5 units (which was our result).
