# The function h= - 16t^{2} + 48t represents the height h (in feet) of a kickball t seconds after it is kicked from the ground. a) Find the maximum height of the kickball. b) Find and interpet the axis of symmetry.

The function represents the height h (in feet) of a kickball t seconds after it is kicked from the ground. a) Find the maximum height of the kickball. b) Find and interpet the axis of symmetry.
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Delorenzoz

a) Concept used: Maximum or minimum value of the function.

Calculation: On comparing the equation ,

Since,

The function has minimum value. For minimum value, Calculate t, $t=\frac{-b}{2a}$ Therefore, $t=\frac{-\left(48\right)}{2\left(-16\right)}$ So, $t=\frac{-48}{-32}$

On substituting $t=\frac{3}{2}$ in equation.

On squaring,

On solving,

Therefore, $t=36$

b) Concept used: Formula for axis of symmetry, $t=\frac{-b}{2a}.$

Calculation: On comparing the equation

Calculate the axis of symmetry, $t=\frac{-b}{2a}$

Therefore, $t=\frac{-48}{2\left(-16\right)}$

So, $t=\frac{-48}{-32}$

The axis of symmetry, $t=\frac{3}{2}$