Algebra II : Polynomial Functions

Study concepts, example questions & explanations for Algebra II

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Example Questions

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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)?

Possible Answers:

Correct answer:

Explanation:

The highest point of the ball is the vertex of the ball's parabolic path, so to find the number of seconds  that is takes to reach this point, it is necessary to find the vertex of the parabola of the graph of the function

The parabola of the graph of 

has as its ordinate, or -coordinate,

,

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 #32 : 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)?

Possible Answers:

Correct answer:

Explanation:

When the baseball hits the ground, its height is 0; therefore, we are looking for  such that 

,

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:

Possible Answers:

Correct answer:

Explanation:

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 #34 : Polynomial Functions

What are the roots of ?

Possible Answers:

Correct answer:

Explanation:

In order to find the roots, we must factor the equation.

The factors of this equation are  and .

Setting those two equal to zero, we get  and .

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