Algebra II : Polynomial Functions
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Example Question #31 : Polynomial Functions
A baseball is thrown off the roof of a building 220 feet high at an initial upward speed of 72 feet per second; the height of the baseball relative to the ground is modeled by the function
How long does it take for the baseball to reach its highest point (nearest tenth of a second)?
The highest point of the ball is the vertex of the ball's parabolic path, so to find the number of seconds 
The parabola of the graph of
has as its ordinate, or 
so, setting 
which rounds to 2.3 seconds. This is the time that it takes the ball to reach the highest point of its path.
Example Question #31 : Polynomial Functions
A baseball is thrown off the roof of a building 220 feet high at an initial upward speed of 72 feet per second; the height of the baseball relative to the ground is modeled by the function
How long does it take for the baseball to hit the ground (nearest tenth of a second)?
When the baseball hits the ground, its height is 0; therefore, we are looking for 
or
This equation can most easily be solved using the quadratic formula. If
then
Setting 
One possible answer is
We throw this out, since we cannot have "negative time".
The other is
This is positive, so we accept this answer. The ball hits the ground in about 6.6 seconds.
Example Question #33 : Polynomial Functions
Find the product:
Using the FOIL (first, outer, inner, last) method, you can expand the polynomial to get
first:
outer:
inner:
lasts:
From here, combine the like terms.
Example Question #581 : Functions And Graphs
What are the roots of 
In order to find the roots, we must factor the equation.
The factors of this equation are 
Setting those two equal to zero, we get 
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