If a projectile is fired straight upward from the ground with an initial speed of 96 feet per second, then its height h in feet after t seconds is given by the function h(t)= -16t^2 + 96t. Find the maximum height of the projectile.

Now, for quadratic equations, the max value occurs at [tex]x=-\frac{b}{2a}[/tex] and the max value is what we get when we put that number in the function. First, lets find the value on which is occurs:

[tex]x=-\frac{b}{2a}\\x=-\frac{96}{2(-16)}\\x=3[/tex]

Now, put x = 3 into the equation:

[tex]h(t)=-16t^2+96t\\h(3)=-16(3)^2+96(3)\\h(3)=144[/tex]

The max height of projectile is 144 feet

If a projectile is fired straight upward from the ground with an initial speed of 96 feet per​ second, then its height h in feet after t seconds is given by the function ​h(t)= -16t^2 + 96t. Find the maximum height of the projectile.

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If a projectile is fired straight upward from the ground with an initial speed of 96 feet per second, then its height h in feet after t seconds is given by the function h(t)= -16t^2 + 96t. Find the maximum height of the projectile.