By definition of the zeros of ta quadratic function, for 5.5 seconds the ball is in the air before it hits the ground.
Zeros of a function
The points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.
That is, the zeros represent the roots of the polynomial equation that is obtained by making f(x)=0.
In summary, the roots or zeros of the quadratic function are those values of x for which the expression is equal to 0. Graphically, the roots correspond to the abscissa of the points where the parabola intersects the x-axis.
Time the ball is in the air before it hits the ground
In this case, the height "h" of a ball thrown straight up with a velocity of 88 ft/s is given by h = -16t² + 88t, where "t" is the time it is in the air.
When the ball hits he ground, he height h has a value of zero. This is h=0. Replacing in the previous expression for the height you get:
0= -16t² + 88t
It can be solved by extracting the term "t" as a common factor:
0= t×(-16t + 88)
The Zero Product Principle says that if the product of two numbers is 0, then at least one of the factors is 0. Then:
t= 0
or
0= -16t + 88
Solving: -88= -16t
(-88)÷ (-16)=t
5.5= t
Finally, this means that for 5.5 seconds the ball is in the air before it hits the ground.
Learn more about the zeros of a quadratic function:
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