Algebra II : Graphing Polynomial Functions

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #53 : Polynomial Functions

How many -intercepts does the graph of the following function have?

Possible Answers:

Ten

Zero

Five

One 

Two

Correct answer:

One 

Explanation:

The graph of a quadratic function  has an -intercept at any point  at which , so, first, set the quadratic expression equal to 0:

The number of -intercepts of the graph is equal to the number of real zeroes of the above equation, which can be determined by evaluating the discriminant of the equation, . Set , and evaluate:

The discriminant is equal to zero, so the quadratic equation has one real zero, and the graph of  has exactly one -intercept.

Example Question #54 : Polynomial Functions

The vertex of the graph of the function 

appears in __________.

Possible Answers:

Quadrant III

None of these

Quadrant II

Quadrant I

Quadrant IV

Correct answer:

Quadrant I

Explanation:

The graph of the quadratic function  is a parabola with its vertex at the point with coordinates

.

Set ; the -coordinate is 

.

Evaluate  by substitution:

The vertex has a positive -coordinate and a positive -coordinate, putting it in the upper right quadrant, or Quadrant I.

Example Question #55 : Polynomial Functions

The vertex of the graph of the function 

appears in __________.

Possible Answers:

Quadrant IV

Quadrant III

Quadrant II

None of these

Quadrant I

Correct answer:

Quadrant III

Explanation:

The graph of the quadratic function  is a parabola with its vertex at the point with coordinates

.

Set ; the -coordinate is .

Evaluate  by substitution:

The vertex has a negative -coordinate and a negative -coordinate, putting it in the lower left quadrant, or Quadrant III.

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